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Skelton, RWOS:000252251606130EMass optimized selfactuated panels for several truss core topologiesWOS:000252251606101DPROCEEDINGS OF THE SEVENTEENTH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETEWOS:000281596300084D2005 44th IEEE Conference on Decision and Control & European ControlWOS:000240653707151:Dynamic simulation of a spatial 3DOF tensegrity mechanismWOS:000235377900002WOS:00023328250001410.1115/1.1913705)Active control of a tensegrity plane gridWOS:000240653706099EControlling instability with delayed antagonistic stochastic dynamicsCabrera, JL4PHYSICA ASTATISTICAL MECHANICS AND ITS APPLICATIONSWOS:000231574400006 0378437110.1016/j.physa.2005.05.007(Static analysis of tensegrity structuresWOS:00022878190001210.1115/1.18041943Inputoutput selection for planar tensegrity models/IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGYWOS:000231543800010 1063653610.1109/TCST.2005.847346CA new topology of tensegrity towers with uniform force distributionASmart Structures and Materials 2005: Modeling, Signal Processing,WOS:000230407700018 0277786X10.1117/12.598265 An active, structure that learnsWOS:000225927600002%10.1016/(ASCE)08873801(2005)19:1(16):Structural behavior and design methods of Tensegrity domes(JOURNAL OF CONSTRUCTIONAL STEEL RESEARCHWOS:000225522200002 0143974X10.1016/j.jcsr.2004.06.004,Stability of an elastic tensegrity structureWOS:00023276320000110.1007/s00707005024405Stability of an elastic cytoskeletal tensegrity modelWOS:00022753660002110.1016/j.ijsolstr.2004.11.008=Inducing reversible stiffness changes in DNAcrosslinked gelsJOURNAL OF MATERIALS RESEARCHWOS:000229671500013 0884291410.1557/JMR.2005.0186WOS:00023040770001710.1117/12.600582?Simultaneous structure and control optimization of tensegritiesASMART STRUCTURES AND MATERIALS 2005: MODELING, SIGNAL PROCESSING,WOS:000230407700013(JOURNAL OF GUIDANCE CONTROL AND DYNAMICSWOS:000229031100004 07315090!Algebraic tensegrity formfinding1617WOS:00022965990001710.1016/j.ijsolstr.2005.01.014?Integrated structure and control design of modular tensegritiesD2005 44TH IEEE CONFERENCE ON DECISION AND CONTROL & EUROPEAN CONTROLWOS:000240653707150DSmart Structures and Materials 2005: Smart Structures and IntegratedWOS:00023033880002610.1117/12.5699790+Gait production in a tensegrity based robot72005 12th International Conference on Advanced RoboticsWOS:000234272400033PHYSICAL REVIEW EWOS:000232930600090 1539375510.1103/PhysRevE.72.041927*Dynamics and control of tensegrity systems@IUTAM Symposium on Vibration Control of Nonlinear Mechanisms andWOS:0002351630000289Shape change of tensegrity structures: Design and controlBACC: PROCEEDINGS OF THE 2005 AMERICAN CONTROL CONFERENCE, VOLS 17WOS:000231947703043
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TypeTitleAuthorsSourceVolumeIssueBegin PgEnd PgYearTCAbstract Access NISSNDOItOn the singularities of a constrained (incompressiblelike) tensegritycytoskeleton model under equitriaxial loadingODesign of tensegrity structures using parametric analysis and stochastic searchThe cytoskeletal organization of breast carcinoma and fibroblast cells inside three dimensional (3D) isotropic silicon microstructuresrIntermediate filamentdeficient cells are mechanically softer at large deformation: A multiscale simulation study]A Monte Carlo formfinding method for large scale regular and irregular tensegrity structuresaDETERMINATION OF THE ANALYTICAL WORKSPACE BOUNDARIES OF A NOVEL 2DOF PLANAR TENSEGRITY MECHANISMMSelfassembly of threedimensional prestressed tensegrity structures from DNA{Control of a Seismically Excited Benchmark Building Using Linear Matrix InequalityBased Semiactive Nonlinear Fuzzy ControloProportional damping approximation using the energy gain and simultaneous perturbation stochastic approximationHigh magnetic gradient environment causes alterations of cytoskeleton and cytoskeletonassociated genes in human osteoblasts cultured in vitronAbnormal fiber end migration in Royal College of Surgeons rats during posterior subcapsular cataract formationVImmunohistochemical Aspects of the Fibrogenic Pathway in Nephrogenic Systemic FibrosisImplicit mechanistic role of the collagen, smooth muscle, and elastic tissue components in strengthening the air and blood capillaries of the avian lungQKinematic and static analysis of a 3PU(P)underbarS spatial tensegrity mechanismNSymmetric prismatic tensegrity structures: Part I. Configuration and stabilityMEXPLORING CELLULAR TENSEGRITY: PHYSICAL MODELING AND COMPUTATIONAL SIMULATIONDesigning structures for dynamical properties via natural frequencies separation Application to tensegrity structures designIDynamic Workspace and Control of Planar Active Tensegritylike StructuresHTensegrity as a Structural Framework in Life Sciences and BioengineeringMAutomated discovery and optimization of large irregular tensegrity structures[On the singularities of constrained tensegrity systems  application to a modified T3 modelqSTUDY THE EFFECT OF ANTICANCER DRUGS ON HUMAN BREAST CANCER CELLS USING THREE DIMENSIONAL SILICON MICROSTRUCTURESJCPG Control of a Tensegrity Morphing Structure For Biomimetic App< licationsxOn Characterizations of Rigid Graphs in the Plane Using Spanning Trees On Characterizations of Rigid Graphs in the PlanecLogarithmic strain measure applied to the nonlinear positional formulation for space truss analysisWFormation shape and orientation control using projected collinear tensegrity structuressTensegrity Structures with Buckling Members Explain Nonlinear Stiffening and Reversible Softening of Actin NetworksHOW AN EUKARYOTIC CELL SENSES THE SUBSTRATE STIFFNESS? AN EXPLORATION USING A FINITE ELEMENT MODEL WITH CYTOSKELETON MODELLED AS TENSEGRITY STRUCTUREQMechanisms of prestressed reticulate systems with unilateral stiffened componentsUDNAbased nanostructures: Changes of mechanical properties of DNA upon ligand bindingcTwo general methods for creating tensegrity structures of towers, arches, bridges and stadium roofsdComparison between experimental tests and numerical simulations carried out on a tensegrity minigrid_Kinematic and static analysis of a threedegreeoffreedom spatial modular tensegrity mechanismOKinematics, dynamics and control of a planar 3DOF tensegrity robot manipulatorVA method to generate stable, collision free configurations for tensegrity based robotsRActive tensegrity: A control framework for an adaptive civilengineering structureHDynamic Workspace and Control of Planar Active Tensegritylike StructuresMKinematic Analysis of a Planar Tensegrity Mechanism with PreStressed SpringsbDomain decomposition approach for nonsmooth discrete problems, example of a tensegrity structureSReversible switching of hydrogelactuated nanostructures into complex micropatternsQKinematic and dynamic analysis of a spatial oneDOF foldable tensegrity mechanismSTensegrity structures in the design of flexible structures for offshore aquacultureRDirect mechanical measurement of geodesic structures in rat mesenchymal stem cellsVLearning, selfdiagnosis and multiobjective control of an active tensegrity structureaKinematic, static, and dynamic analysis of a spatial threedegreeoffreedom tensegrity mechanismMKinematic, static and dynamic analysis of a planar 2DOF tensegrity mechanismYFormfinding of complex tensegrity structures: application to cell cytoskeleton modellingUMolecular geometry from molecular tensegrity: A case study of gasphase MX2 compoundsiMolecular tensegrity: predicting 1,3XX distance in gasphase MXn (n <= 4) compounds from atomic sizesNModel of mechanical interaction of mesenchyme and epithelium in living tissuesQOn the elastica solution of a tensegrity structure: Application to cell mechanicsWSelection of prestress for optimal dynamic/control performance of tensegrity structuresHA direct approach to design of geometry and forces of tensegrity systemsOAdaptive force density method for formfinding problem of tensegrity structuresIForm finding analysis of tensgrity structures based on variational methodLKinematic and static analysis of a planar modular 2DoF tensegrity mechanismXBacklashfree motion control of robotic manipulators driven by tensegrity motor networksTA Semidefinite Programming Approach to Tensegrity Theory and Realizability of Graphs`Timeenergy optimal control of hyperactuated mechanical systems with geometric path constraints^Kinematic, static, and dynamic analysis of a planar onedegreeoffreedom tensegrity mechanismNAccurate simulation of nearwall turbulence over a compliant tensegrity fabricJPath planning and openloop shape control of modular tensegrity structuresqNonequilibrium statistical mechanical models for cytoskeletal assembly: Towards understanding tensegrity in cellsMRedundancy in the control of robots with highly coupled mechanical structureslMechanical response of a tensegrity structure close to its integrity limit submitted to external constraintsQConstraining plane configurations in CAD: Circles, lines, and angles in the planeTEconomic sensor/actuator selection and its application to flexible structure control^Control/structure optimization approach for minimumtime reconfiguration of tensegrity systemsNControl synthesis for a class of light and agile robotic tensegrity structuresrCombining dynamic relaxation method with artificial neural networks to enhance simulation of tensegrity structuresChange of the topography of ventral, cell surface during spreading of fibroblasts as revealed by evanescent waveexcited fluorescence microscopy: Effect of contractility and microtubule integrityJDynamic behavior of a tensegrity system subjected to follower wind loadingoDesign, modeling, and optimization of compliant tensegrity fabrics for the reduction of turbulent skin frictionSGeneral class of tensegrity structures: Topology and prestress equilibrium analysis[On mechanical modeling of dynamic changes in the structure and properties of adherent cellslSpecific mechanical and structural responses of cortical and cytosolic cytoskeleton in living adherent cellsoImprovement of force modulation mode with scanning probe microscopy for imaging viscoelasticity of living cellsJThe reverse displacement analysis of a tensegrity based parallel mechanismWInitial shape finding and modal analyses of cyclic rightcylindrical tensegrity modules[Static and dynamic analyses of tensegrity structures. Part 1. Nonlinear equations of motionTStatic and dynamic analyses of tensegrity structures. Part II. Quasistatic analysishStatic and dynamic characterization of regular truncated icosahedral and dodecahedral tensegrity modulesMInitial shapefinding and modal analyses of cyclic frustum tensegrity modulesPThe prestressability problem of tensegrity structures: some analytical solutionsQA visualization method for the morphological exploration of tensegrity structures~Biological design principles that guide selforganization, emergence, and hierarchical assembly: From complexity to tensegritynRole of cellular tone and microenvironmental conditions on cytoskeleton stiffness assessed by tensegrity modelQStructural approach of cytoskeletal mechanics: cellular solid vs tensegrity model\Influence of laminar shear stress on cytoskeleton and ICAM1 expression of endothelial cellsXA tensegrity structure with buckling compression elements: Application to cell mechanicsIDoublelayer grids: Review of dynamic analysis methods and special topicsNCONFIGURATIONS OF FEW LINES IN 3SPACE  ISOTOPY, CHIRALITY AND PLANAR LAYOUTSIDOUBLELAYER TENSEGRITY GRIDS  STATIC LOAD RESPONSE .1. ANALYTICAL STUDYKDOUBLELAYER TENSEGRITY GRIDS  STATIC LOAD RESPONSE .2. EXPERIMENTALSTUDYaFULLER,BUCKMINSTER TENSEGRITY STRUCTURES AND MAXWELL,CLERK RULES FOR CONSTRUCTION OF STIFF FRAMESDense filling type tensegrity joint for tensegrity structure, has coated tension portions, each converge into guidance slit facing across cylindrical tunnelMethod of converting tensegrity structure into musical instrument, involves tying struts together at internal strut nodal minimum of desired resonate modes of strutsArchitectural element for covering infrastructure e.g. element of roof, has grid having strips so that height of strip is less than half of width to fasten strips to membrane supported by gridAssembly holder for constructing tensegrity structure before/during attachment of steel cable components to pressure rods comprises geometric axis that forms at each end of the holder the normal of the axis of pressure elementSpherical dodecahedral enclosure used as e.g. building, pressure vessel, vacuum vessel, liquid or gas container, has twenty band intersections covered and/or sealed to form airtight seal, and seams sealed to make the enclosure airtightJoint for use in foldable tensegrity structure, has joint main body for connecting tiltable rods, in which tilting center of each rod is positioned on circular track and connection rod is arranged at central point of circular trackBase module for spatial structure comprises six rigid bars with tips linked by pretensioned cables to form polyhedron with triangular facestThreads for holding rods in Tensegrity constructionhas threads located in slotted e< nds of rods with retaining knotsTensegrity structurehas tensegrity module including several compression materials that surround tension materials and meander along stretch direction of tension materialsTriangular shape module for tensegrity structure constructionhas wire rod which couples central poles of upper and lower surfaceReadily erectable building structuresincludes roof structure incorporating stressed cables and compressed struts with structure supported by lugsqSpiral helix tensegrity domehas all junction points precisely located from jig for construction with top closureModular polyhedral building elementscomprises compression and tension elements defining polyhedron and interconnecting other modules$Bliss, TK; Iwasaki, T; BartSmith, HBursa, J; Fuis, VFNechipurenko, Y; Grokhovsky, S; Gursky, G; Nechipurenko, D; Polozov, RZhou, Y; Xie, YM; Huang, X Villard, PF; Bourne, W; Bello, FAliawdin, P; Silicka, E'Yu, CH; Haller, K; Ingber, D; Nagpal, RJuan, SH; Tur, JMM)Crane, CD; Bayat, J; Vikas, V; Roberts, RNabet, B; Leonard, NEMasters, B; Wade, DAdam, B; Smith, IFCGoto, K; Noguchi, HZhang, JY; Ohsaki, MFujii, M; Yoshii, S; Kakazu, Yde Oliveira, MC; Skelton, RELuo, HX; Bewley, TRMasic, M; Skelton, REMoored, KW; BartSmith, HPaul, C; Lipson, H; Cuevas, FJV.Chan, WL; Arbelaez, D; Bossens, F; Skelton, RE"Pinaud, JP; Solari, S; Skelton, RESkelton, RE; Li, FMBayat, J; Crane, CDAldrich, JB; Skelton, REMurakami, H; Nishimura, Y!Pinaud, JP; Masic, M; Skelton, RE*Zaslavsky, R; de Oliveira, MC; Skelton, REChan, WL; Skelton, REMasic, MR; Skelton, RE"Skelton, RE; Williamson, D; Han, JTran, T; Crane, CD; Duffy, JMotro, R; Vassart, NBouderbala, M; Motro, R?Muller, S; Sun, R; Legrand, S; Labrador, V; Wang, X; Stoltz, JFLiu, YX; Lu, ZT/Campbell, DM; Chen, D; Gossen, PA; Hamilton, KPCHEN, PS; ABE, M; KAWAGUCHI, MLEVY, M; TERRY, W; JING, TF!Li, Y; Feng, XQ; Cao, YP; Gao, HJ,Zhang, JY; Guest, SD; Connelly, R; Ohsaki, MCao, QS; Zhang, ZH#Doray, F; Karpenkov, O; Schepers, JSkelton, RE; de Oliveira, MCTran, HC; Lee, JEhara, S; Kanno, YPirentis, AP; Lazopoulos, KAXu, X; Luo, YZ7RhodeBarbarigos, L; Jain, H; Kripakaran, P; Smith, IFC+Nikkhah, M; Strobl, JS; De Vita, R; Agah, MAli, NBH; Smith, IFC3RhodeBarbarigos, L; Ali, NBH; Motro, R; Smith, IFCVychytil, J; Holecek, MBertaud, J; Qin, Z; Buehler, MJRecski, A; Shai, OCefalo, M; Tur, JMMWolff, L; Fernandez, P; Kroy, K5Liedl, T; Hogberg, B; Tytell, J; Ingber, DE; Shih, WM Kim, Y; Langari, R; Hurlebaus, S!Munoz, JJ; Conte, V; Miodownik, M(Feng, XQ; Li, Y; Cao, YP; Yu, SW; Gu, YT Jamali, Y; Azimi, M; Mofrad, MRKCSevercan, I; Geary, C; Chworos, A; Voss, N; Jacovetty, E; Jaeger, LOQian, AR; Yang, PF; Hu, LF; Zhang, W; Di, SM; Wang, Z; Han, J; Gao, X; Shang, P"Joy, A; Mohammed, TA; AlGhoul, KJJonas, O; Duschl, C5Quatresooz, P; Paquet, P; HermannsLe, T; Pierard, GELobo, D; Vico, FJMaina, JN; Jimoh, SA; Hosie, MTur, JMM; Juan, SHArsenault, M; Gosselin, CMZhang, JY; Guest, SD; Ohsaki, MyZheng, CH; Doll, J; Gu, E; HagerBarnard, E; Huang, Z; Kia, A; Ortiz, M; Petzold, B; Usul, T; Kwon, R; Jacobs, C; Kuhl, ESchmalz, AP; Agrawal, SK'Rieffel, J; ValeroCuevas, F; Lipson, H9Pirentis, AP; Markatis, S; Lazopoulos, KA; Lazopoulos, AK!Panigrahi, R; Gupta, A; Bhalla, SNikkhah, M; Strobl, JS; Agah, MRovira, AG; Tur, JMMPagitz, M; Tur, JMMGreco, M; Ferreira, IPPais, D; Cao, M; Leonard, NE!Jordan, T; Recski, A; Szabadka, Z+Maurin, B; Motro, R; Cevaer, F; Raducanu, V
Xu, X; Luo, Y/Angellier, N; Dube, JF; Quirant, J; Crosnier, BShibata, M; Saijyo, F; Hirai, SRDe Santis, G; Boschetti, F; Lennon, AB; Prendergast, PJ; Verdonck, P; Verhegghe, B Maurin, B; Bagneris, M; Motro, R&Yuan, XF; Peng, ZL; Dong, SL; Zhao, BJ#Dube, JF; Angellier, N; Crosnier, B'Frigola, R; Ros, L; Roure, F; Thomas, FCvon Kruger, PG; Rodrigues, FC; Moreira, LE; Carrasco, EVM; Greco, MVasquez, RE; Correa, JCSohi, MA; Behzadipour, S3Grillo, F; Calvaruso, S; Severino, R; Serrecchia, SJJeong, B; Park, JS; Lee, KJ; Hong, SC; Hyon, JY; Choi, H; Ahn, DJ; Hong, S!Nineb, S; Alart, P; Dureisseix, DRaja, MG; Narayanan, S>Sidorenko, A; Krupenkin, T; Taylor, A; Fratzl, P; Aizenberg, J Schenk, M; Guest, SD; Herder, JLSwartz, MA; Hayes, MJDMicheletti, A; Williams, WOFJensen, O; Wroldsen, AS; Lader, PF; Fredheim, A; Heide, M; Johansen, VTur, JMM; Juan, SH; Rovira, AG^Maguire, P; Kilpatrick, JI; Kelly, G; Prendergast, PJ; Campbell, VA; O'Connell, BC; Jarvis, SP(Rieffel, J; Lipson, H; ValeroCuevas, FJRBaudriller, H; Maurin, B; Canadas, P; Montcourrier, P; Parmeggiani, A; Bettache, NDe Guzman, M; Orden, Dde Jager, B; Skelton, REEriksson, A; Tibert, AG'Estrada, GG; Bungartz, HJ; Mohrdieck, CLazopoulos, KA; Lazopoulou, NKMasic, M; Skelton, RE; Gill, PE%Paul, C; ValeroCuevas, FJ; Lipson, HZhang, L; Maurin, B; Motro, RZhang, JY; Ohsaki, M; Kanno, YLi, FM; Skelton, RE0Moored, KW; Taylor, SA; Bliss, TK; BartSmith, H&de Oliveira, MC; Skelton, RE; Chan, WL*Wroldsen, AS; de Oliveira, MC; Skelton, REScruggs, JT; Skelton, RESo, AMC; Ye, YY,Averseng, J; Dube, JF; Crosnier, B; Motro, RCrane, CD; Duffy, J; Correa, JCDomer, B; Smith, IFCLin, DC; Yurke, B; Langrana, NA&Masic, M; Skelton, RE; de Oliveira, MC,Paul, C; Roberts, JW; Lipson, H; Cuevas, FJVShen, TY; Wolynes, PGvan de Wijdeven, J; de Jager, BPaul, C; Lipson, HFest, E; Shea, K; Smith, IFCSaliola, F; Whiteley, WSultan, C; Skelton, R+Aldrich, JB; Skelton, RE; KreutzDelgado, K!Connelly, R; Demaine, ED; Rote, G)Domer, B; Raphael, B; Shea, K; Smith, IFC'Domer, B; Fest, E; Lalit, V; Smith, IFC&Fest, E; Shea, K; Domer, D; Smith, IFCHirata, H; Ohki, K; Miyata, H4Lazzari, M; Vitaliani, RV; Majowiecki, M; Saetta, AV$Quirant, J; KaziAoual, MN; Motro, RWilliamson, D; Skelton, RE"Williamson, D; Skelton, RE; Han, J=Bradshaw, R; Campbell, D; Gargari, M; Mirmiran, A; Tripeny, P"de Jager, B; Skelton, RE; Masic, MGasparini, D; Gautam, V"Kanchanasaratool, N; Williamson, D7Laurent, VM; Fodil, R; Canadas, P; Planus, E; Isabey, DANagayama, M; Haga, H; Tanaka, Y; Hirai, Y; Kabuto, M; Kawabata, KShea, K; Fest, E; Smith, IFC"Sultan, C; Corless, M; Skelton, RETibert, AG; Pellegrino, SYuan, XF; Dong, SLAdriaenssens, SML; Barnes, MR#Connelly, R; Rybnikov, K; Volkov, Sde Jager, B; Skelton, RNishimura, Y; Murakami, HOppenheim, IJ; Williams, WO$Skelton, RE; Pinaud, JP; Mingori, DL:Skelton, RE; Adhikari, R; Pinaud, JP; Chan, WL; Helton, JWBen Kahla, N; Kebiche, KKWendling, S; Planus, E; Laurent, VM; Barbe, L; Mary, A; Oddou, C; Isabey, D Wendling, S; Oddou, C; Isabey, D3Williams, DP; Carlson, WB; Schulze, WA; Pilgram, SM(Knight, B; Duffy, J; Crane, C; Rooney, J%Carlson, WB; Williams, D; Newnham, RE$Kawaguchi, M; Tatemichi, I; Chen, PS$Kebiche, K; KaziAoual, MN; Motro, RConnelly, R; Back, A+Djouadi, S; Motro, R; Pons, JS; Crosnier, BGaspar, Z; Radics, N; Recski, A Moussa, B; Pons, JC; Crosnier, BCoughlin, MF; Stamenovic, D2Terry, WR; Storm, GA; Houghton, KM; Hofmeister, WSConnelly, R; Whiteley, WMalla, RB; Serrette, RLRECSKI, A; SCHWARZLER, WCalladine, CR; Pellegrino, SHANAOR, A; LIAO, MKROTH, B; WHITELEY, WThis study aimed to develop a method to construct tensegrity structures from elementary cells, defined as structures consisting of only one bar connected with a few strings. Comparison of various elementary cells leads to the further selection of the socalled 'Zshaped' cell, which contains one bar and three interconnected strings, as the elementary module to assemble the Zbased spatial tensegrity structures. The graph theory is utilized to analyse the topology of strings required to construct this type of tensegrity structures. It is shown that 'a string net can be used to construct a Zbased tensegrity structure if and only if its topology is a simple and bridgeless cubic graph'. Once the topology of strings has < been determined, one can easily design the associated tensegrity structure by adding a deterministic number of bars. Two schemes are suggested for this design strategy. One is to enumerate all possible topologies of Zbased tensegrity for a specified number of bars or cells, and the other is to determine the tensegrity structure from a vertextruncated polyhedron. The method developed in this paper allows us to construct various types of novel tensegrity structures.This paper presents conditions for selfequilibrium and super stability of dihedral 'star' tensegrity structures, based on their dihedral symmetry. It is demonstrated that the structures are super stable if and only if they have an odd number of struts, and the struts are as close as possible to each other. Numerical investigations show that their prestress stability is sensitive to the geometry realisation. (C) 2010 Published by Elsevier Ltd.The suspendome has been widely used as the structural roof system of sports buildings in recent years. It is a kind of hybrid space structure composed of an upper rigid singlelayer latticed shell and a lower flexible tensegrity (cablestrut) system. The prestress level in the lower cablestrut system is of great significance for the suspendome structure because it has no initial geometric stiffness (for a ribring type) before prestress is introduced into the lower tensegrity system. The traditional solution for calculating the selfinternalforce mode and the prestress force level (force finding) is somewhat complicated; in general it is based on the Equilibrium Matrix Theory. In the present paper, a simplified computational strategy for the determination of the selfinternalforce mode based on the nodal equilibrium is presented for the tensegrity system in a suspendome which is grounded on a newly developed method: the Local Analysis Method. Two types of cablestrut arrangement, the Levy system and the Geiger system, are addressed, and the characteristic of each type is expounded. An analytical solution for the selfinternalforce mode of the lower cablestrut system is put forward together with the equivalent nodal force acting on the upper singlelayer dome for the two types of cablestrut arrangement. The determination of the prestress level of the lower tensegrity system is then elucidated on the ground of the initial architectural configuration. the counterbalance of the bearing reaction, the equivalent nodal force, and the windinduced slackening effect. An illustrative example is appended in the end to validate the efficiency of this simplified method. It is shown that force finding, at the viewpoint of structural design, based on this method is of great accuracy and efficiency. The prestress in the outermost ring generally has the highest level among the cablestrut system, and has the most influence on the structural performance of the suspendome. The results from the studies can be referred to not only for direct design use in practical engineering, but also for the design of similar hybrid space structures. (C) 2009 Elsevier Ltd. All rights reserved.cConsider a graph G with n vertices. In this paper we study geometric conditions for an ntuple of points in a"e (d) to admit a nonzero selfstress with underlying graph G. We introduce and investigate a natural stratification, depending on G, of the configuration space of all ntuples in a"e (d) . In particular we find surgeries on graphs that give relations between different strata. Further we discuss questions related to geometric conditions defining the strata for plane tensegrities. We conclude the paper with particular examples of strata for tensegrities in the plane with a small number of vertices.The usual use of fractals involves selfsimilar geometrical objects to fill a space, where the self similar iterations may continue ad infinitum. This is the first paper to propose the use of selfsimilar mechanical objects that fill an alloted space, while achieving an invariance property as the selfsimilar iterations continue (e.g. invariant strength). Moreover, for compressive loads, this paper shows how to achieve minimal mass and invariant strength from selfsimilar structures. The topology optimization procedure uses selfsimilar iteration until minimal mass is achieved, and this problem is completely solved, with global optimal solutions given in closed form. The optimal topology remains independent of the magnitude of the load. Mass is minimized subject to yield and/or buckling constraints. Formulas are also given to optimize the complexity of the structure, and the optimal complexity turns out to be finite. That is, a continuum is never the optimal structural for a compressive load under any constraints on the physical dimension (diameter). After each additional selfsimilar iteration, the number of bars and strings increase, but, for a certain choice of unit topology shown, the total mass of bars and strings decreases. For certain structures, the string mass monotonically increases with iteration, while the bar mass monotonically reduces, leading to minimal total mass in a finite number of iterations, and hence a finite optimal complexity for the structure. The number of iterations required to achieve minimal mass is given explicitly in closed form by a formula relating the chosen unit geometry and the material properties. It runs out that the optimal structures produced by our theory fall in the category of structures we call tensegrity. Hence our selfsimilar algorithms can generate tensegrity fractals. (c) 2009 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.CThis paper provides the closed form analytical solution to the problem of minimizing the material volume required to support a given set of bending loads with a given number of discrete structural members, subject to material yield constraints. The solution is expressed in terms of two variables, the aspect ratio, rho(1), and complexity of the structure, q (the total number of members of the structure is equal to q(q + 1)). The minimal material volume (normalized) is also given in closed form by a simple function of rho and q, namely, V = q(rho(1/q)  rho(1/q)). The forces for this nonlinear problem are shown to satisfy a linear recursive equation, from nodetonode of the structure. All member lengths are specified by a linear recursive equation, dependent only on the initial conditions involving a user specified length of the structure. The final optimal design is a class 2 tensegrity structure. Our results generate the 1904 results of Michell in the special case when the selected complexity q approaches infinity. Providing the optimum interms of a given complexity has the obvious advantage of relating complexity q to other criteria, such as costs, fabrication issues, and control. If the structure is manufactured with perfect joints (no glue, welding material, etc.), the minimal mass complexity is infinite. But in the presence of any joint mass, the optimal structural complexity is finite, and indeed quite small. Hence, only simple structures (low complexity q) are needed for practical design. (c) 2009 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.A numerical method is presented for formfinding of tensegrity structures. The topology and the types of members are the only information that requires in this formfinding process. The eigenvalue decomposition of the force density matrix and the single value decomposition of the equilibrium matrix are performed iteratively to find the feasible sets of nodal coordinates and force densities which satisfy the minimum required rank deficiencies of the force density and equilibrium matrices, respectively. Based on numerical examples it is found that the proposed method is very efficient and robust in searching selfequilibrium configurations of tensegrity structures. (C) 2009 Elsevier Ltd. All rights reserved.This paper presents a numerical method for finding a tensegrity structure based on the ground structure method. We first solve a mixed integer programming (MIP) problem which maximizes the number of struts over the selfequil< ibrium condition of axial forces and the discontinuity condition of struts. Subsequently we solve the minimization problem of the number of cables in order to remove redundant selfequilibrium modes, which is also formulated as an MIP. It is regarded to be advantageous that our method does not require any connectivity information of cables and struts to be known in advance, while the obtained tensegrity structure is guaranteed to satisfy the discontinuity condition of struts rigorously. (C) 2009 Elsevier Ltd. All rights reserved.Singularity theory is applied for the study of the characteristic threedimensional tensegritycytoskeleton model after adopting an incompressibility constraint. The model comprises six elastic bars interconnected with 24 elastic string members. Previous studies have already been performed on nonconstrained systems; however, the present one allows for general nonsymmetric equilibrium configurations. Critical conditions for branching of the equilibrium are derived and postcritical behaviour is discussed. Classification of the simple and compound singularities of the total potential energy function is effected. The theory is implemented into the cusp catastrophe for the case of onedimensional branching of the bucklingallowed tensegrity model, and an elliptic umbilic singularity for compound branching of a rigidbar model. It is pointed out that singularity studies with constraints demand a quite different mathematical approach than those without constraints. (C) 2009 Elsevier Ltd. All rights reserved.In this paper, the formfinding problem of nonregular tensegrities was converted into a constrained optimization problem A genetic algorithm was used to solve this problem Two cases of formfinding were considered In the first case, the number of members, the rest lengths of members, the elastic moduli of members and the connectivity of members were given, and the only variables are the initial locations of nodes In the second case, the elastic moduli of members were also treated as variables besides the initial locations of nodes Typical examples were carried out to verify the proposed method (C) 2009 Elsevier Ltd All rights reservedaTensegrity structures are lightweight structures composed of cables in tension and struts in compression. Since tensegrity systems exhibit geometrically nonlinear behavior, finding optimal structural designs is difficult. This paper focuses on the use of stochastic search for the design of tensegrity systems. A pedestrian bridge made of square hollowrope tensegrity ring modules is studied. Two design methods are compared in this paper. Both methods aim to find the minimal cost solution. The first method approximates current practice in design offices. More specifically, parametric analysis that is similar to a gradientbased optimization is used to identify good designs. Parametric studies are executed for each system parameter in order to identify its influence on response. The second method uses a stochastic search strategy called probabilistic global search Lausanne. Both methods provide feasible configurations that meet civil engineering criteria of safety and serviceability. Parametric studies also help in defining search parameters such as appropriate penalty costs to enforce constraints while optimizing using stochastic search. Traditional design methods are useful to gain an understanding of structural behavior. However, due to the many local minima in the solution space, stochastic search strategies find better solutions than parametric studies.@Studying the cytoskeletal organization as cells interact in their local microenvironment is interest of biological science, tissue engineering and cancer diagnosis applications. Herein, we describe the behavior of cell lines obtained from metastatic breast tumor pleural effusions (MDAMB231), normal fibrocystic mammary epithelium (MCF10A), and HS68 normal fibroblasts inside three dimensional (3D) isotropic silicon microstructures fabricated by a singlemask, singleisotropicetch process. We report differences in adhesion, mechanism of force balance within the cytoskeleton, and deformability among these cell types inside the 3D microenvironment. HS68 fibroblasts typically stretched and formed vinculinrich focal adhesions at anchor sites inside the etched cavities. In contrast, MCF10A and MDAMB231 cells adopted the curved surfaces of isotropic microstructures and exhibited more diffuse vinculin cytoplasmic staining in addition to vinculin localized in focal adhesions. The measurement of cells elasticity using atomic force microscopy (AFM) indentation revealed that H568 cells are significantly stiffer (p < 0.0001) than MCF10A and MDAMB231 cells. Upon microtubule disruption with nocodazole, fibroblasts no longer stretched, but adhesion of MCF10A and MDAMB231 within the etched features remained unaltered. Our findings are consistent with tensegrity theory. The 3D microstructures have the potential to probe cytoskeletalbased differences between healthy and diseased cells that can provide biomarkers for diagnostics purposes. (C) 2010 Elsevier Ltd. All rights reserved.Tensegrities are lightweight space reticulated structures composed of cables and struts. Stability is provided by the selfstress state between tensioned and compressed elements. Tensegrity systems have in general low structural damping, leading to challenges with respect to dynamic loading. This paper describes dynamic behavior and vibration control of a fullscale active tensegrity structure. Laboratory testing and numerical simulations confirmed that control of the selfstress influences the dynamic behavior. A multiobjective vibration control strategy is proposed. Vibration control is carried out by modifying the selfstress level of the structure through small movement of active struts in order to shift the natural frequencies away from excitation. The PGSL stochastic search algorithm successfully identifies good control commands enabling reduction of structural response to acceptable levels at minimum control cost. (C) 2010 Elsevier Ltd. All rights reserved.Tensegrity systems are spatial structures composed of tensile and compression components in a selfequilibrated state of prestress The tensegrity concept has already been studied by researchers in various fields over the past decades. A family of tensegrity modules that can offer promising solutions for civil engineering applications such as tensegrity domes, towers and bridges is analyzed. Research into tensegrity systems has resulted in reliable techniques for form finding and structural analysis. However. the tensegrity concept is not yet part of mainstream structural design. This paper presents a design study of a tensegritybased pedestrian bridge The structural performance of the bridge using three tensegrity modules is evaluated through parametric studies Design requirements for pedestrian bridges and results of parametric studies are used to define a design procedure that optimizes section sizes for this type of structure A structural efficiency indicator is proposed and used to compare proposals for feasible bridge configurations Design results illustrate that the hollowrope tensegrity bridge can efficiently meet typical design criteria (C) 2010 Elsevier Ltd. All rights reservedoLiving cells are reinforced by polymer fibers (the socalled cytoskeleton) which ale responsible for their mechanical behaviour There are many evidences that these fibres are prestressed without an external load To include this prestress into mechanical models of living tissues is not an easy task We propose an approach in which the intracellular prestress is maintained by the incompressibility of cells. A simple illustrative structure is studied in older to determine the dependence of stiffness on the level of prestress Some macroscopic models of lime tissues with prestressed cells are formulated The results show a clear dependence of the macroscopic mechanical response on the level of prestress at microscale. The model exhibits some features of lime cells (prestressinduced stiffening. strain hardening) (C) 2009 IMACS. Published < by Elsevier B.V. All rights reservedAThe cell's cytoskeleton, providing cells with structure and shape, consists of different structural proteins, including microtubules, actin microfilaments and intermediate filaments. It has been suggested that intermediate filaments play a crucial role in providing mechanical stability to cells. By utilizing a simple coarsegrained computational model of the intermediate filament network in eukaryotic cells, we show here that intermediate filaments play a significant role in the cell mechanical behavior at large deformation, and reveal mechanistic insight into cell deformation under varying intermediate filament densities. We find that intermediate filamentdeficient cells display an altered mechanical behavior, featuring a softer mechanical response at large deformation while the mechanical properties remain largely unchanged under small deformation. We compare the results with experimental studies in vimentindeficient cells, showing good qualitative agreement. Our results suggest that intermediate filaments contribute to cell stiffness and deformation at large deformation, and thus play a significant role in maintaining cell structural integrity in response to applied stress and strain, in agreement with earlier hypotheses. The simulation results also suggest that changes in the filament density result in profound alterations of the deformation state of the cell nucleus, leading to greater stretch in the direction of loading and greater contraction in the orthogonal direction as the intermediate filament density is increased. Our model opens the door to future studies to investigate disease states, the effects of amino acid mutations and how structural changes at different levels in the cell's structural makeup influence biomechanical properties. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.A numerical method is presented for initial selfstress design of tensegrity grid structures, which is defined as the linear combination of the coefficients of independent selfstress modes. A discussion on proper division of the number of member groups for the purpose of existence of a single integral feasible selfstress mode has been explicitly given. The unilateral properties of the stresses in cables and struts are taken into account. Evaluation of the stability for the structure is also considered. Three numerical examples are presented to demonstrate the efficiency and robustness in searching initial feasible selfstress mode for tensegrity grid structures. (C) 2010 Elsevier Ltd. All rights reserved.The edge set of a graph G is partitioned into two subsets EC boolean OR ES. A tensegrity framework with underlying graph G and with cables for EC and struts for ES is proved to be rigidly embeddable into a onedimensional line if and only if G is 2edgeconnected and every 2vertexconnected component of G intersects both EC and ES. Polynomial algorithms are given for finding an embedding of such graphs and for checking the rigidity of a given onedimensional embedding. (C) 2009 Elsevier Ltd. All rights reserved.This work addresses the problem of realtime selfcollision detection for a movable tensegrity structure We show that it can be tackled as the collision detection between two generic cylinders moving in R3. It is a simplified version of the more general problem of dynamic collision detection between two general shaped rigid bodies in the space Two algorithms are proposed. The first presented approach is based on the exact value of the distance between two cylinders, the second is based on a new theorem which allows to estimate the exact distance for a given maximum desired error. In some circumstances, the second approach can be preferred because faster (C) 2010 Elsevier Ltd. All rights reserved.6A numerical method is presented for formfinding of cablestrut structures. The topology and the types of members are the only information that is required in this formfinding process. Dummy members are used to transform the cablestrut structure with supports into selfstressed system without supports. The requirement on rank deficiencies of the force density and equilibrium matrices for the purpose of obtaining a nondegenerate ddimensional selfstressed structure has been explicitly discussed. The spectral decomposition of the force density matrix and the singular value decomposition of the equilibrium matrix are performed iteratively to find the feasible sets of nodal coordinates and force densities which satisfy the minimum required rank deficiencies of the force density and equilibrium matrices, respectively. Based on numerical examples it is found that the proposed method is very efficient, robust and versatile in searching selfequilibrium configurations of cablestrut structures. Crown Copyright (C) 2010 Published by Elsevier Ltd. All rights reserved.We propose a Monte Carlo formfinding method that employs a stochastic procedure to determine equilibrium configurations of a tensegrity structure. This method does not involve complicated matrix operations or symmetry analysis, works for arbitrary initial configurations, and can handle large scale regular or irregular tensegrity structures with or without material/geometrical constraints. (C) 2010 Elsevier Ltd. All rights reserved.8Tensegrity mechanisms are slowly emerging as potential alternatives to more conventional mechanisms for certain types of applications where a reduced inertia of the mobile parts and a high payload to weight ratio are sought. With this in mind, a twodegreeoffreedom planar tensegrity mechanism is developed using a simple actuation strategy to keep the mechanism in selfstressed configurations. Solutions to the mechanism's direct and inverse kinematic problems are first developed and are then used to determine analytical expressions for its workspace boundaries.We propose a physical model for the nonlinear inelastic mechanics of sticky biopolymer networks with potential applications to inelastic cell mechanics. It consists of a minimal extension of the glassy wormlike chain (GWLC) model, which has recently been highly successful as a quantitative mathematical description of the viscoelastic properties of biopolymer networks and cells. To extend its scope to nonequilibrium situations, where the thermodynamic state variables may evolve dynamically, the GWLC is furnished with an explicit representation of the kinetics of breaking and reforming sticky bonds. In spite of its simplicity, the model exhibits many experimentally established nontrivial features such as powerlaw rheology, stress stiffening, fluidization and cyclic softening effects.Tensegrity, or tensional integrity, is a property of a structure indicating a reliance on a balance between components that are either in pure compression or pure tension for stability(1,2). Tensegrity structures exhibit extremely high strengthtoweight ratios and great resilience, and are therefore widely used in engineering, robotics and architecture(3,4). Here, we report nanoscale, prestressed, threedimensional tensegrity structures in which rigid bundles of DNA double helices resist compressive forces exerted by segments of singlestranded DNA that act as tensionbearing cables. Our DNA tensegrity structures can selfassemble against forces up to 14 pN, which is twice the stall force of powerful molecular motors such as kinesin or myosin(5,6). The forces generated by this molecular prestressing mechanism can be used to bend the DNA bundles or to actuate the entire structure through enzymatic cleavage at specific sites. In addition to being building blocks for nanostructures, tensile structural elements made of singlestranded DNA could be used to study molecular forces, cellular mechanotransduction and other fundamental biological processes.oThis paper investigates the behavior of a seismically excited benchmark building employing magnetorheological dampers operated by a modelbased fuzzy logic controller (MBFLC) formulated in terms of linear matrix inequalities (LMIs). The MBFLC is designed in a systematic way, while the traditional modelfree fuzz< y logic controller is designed via trial and error by experienced investigators. It is demonstrated from comparison of the uncontrolled and semiactive controlled responses that the proposed LMIbased MBFLC is effective in vibration reduction of a benchmark building under various earthquake loading conditions.A set of equilibrium equations is derived for the stresscontrolled shape change of cells due to the remodelling and growth of their internal architecture. The approach involves the decomposition of the deformation gradient into an active and a passive component; the former is allowed to include a growth process, while the latter is assumed to be hyperelastic and masspreserving. The two components are coupled with a control function that provides the required feedback mechanism. The balance equations for general continua are derived and, using a variational approach, we deduce the equilibrium equations and study the effects of the control function on these equations. The results are applied to a truss system whose function is to simulate the cytoskeletal network constituted by myosin microfilaments and microtubules, which are found experimentally to control shape change in cells. Special attention is paid to the conditions that a thermodynamically consistent formulation should satisfy. The model is used to simulate the multicellular shape changes observed during ventral furrow invagination of the Drosophila melanogaster embryo. The results confirm that ventral furrow invagination can be achieved through stress control alone, without the need for other regulatory or signalling mechanisms. The model also reveals that the yolk plays a distinct role in the process, which is different to its role during invagination with externally imposed strains. In stress control, the incompressibility constraint of the yolk leads, via feedback, to the generation of a pressure in the ventral zone of the epithelium that eventually eases its rise and internalisation.As a special type of novel flexible structures, tensegrity holds promise for many potential applications in such fields as materials science, biomechanics, civil and aerospace engineering. Rhombic systems are an important class of tensegrity structures, in which each bar constitutes the longest diagonal of a rhombus of four strings. In this paper, we address the design methods of rhombic structures based on the idea that many tensegrity structures can be constructed by assembling onebar elementary cells. By analyzing the properties of rhombic cells, we first develop two novel schemes, namely, direct enumeration scheme and cellsubstitution scheme. In addition, a facile and efficient method is presented to integrate several rhombic systems into a larger tensegrity structure. To illustrate the applications of these methods, some novel rhombic tensegrity structures are constructed.eUnderstanding the biomechanical properties and the effect of biomechanical force on epithelial cells is key to understanding how epithelial cells form uniquely shaped structures in two or threedimensional space. Nevertheless, with the limitations and challenges posed by biological experiments at this scale, it becomes advantageous to use mathematical and 'in silico' (computational) models as an alternate solution. This paper introduces a singlecellbased model representing the cross section of a typical tissue. Each cell in this model is an individual unit containing several subcellular elements, such as the elastic plasma membrane, enclosed viscoelastic elements that play the role of cytoskeleton, and the viscoelastic elements of the cell nucleus. The cell membrane is divided into segments where each segment (or point) incorporates the cell's interaction and communication with other cells and its environment. The model is capable of simulating how cells cooperate and contribute to the overall structure and function of a particular tissue; it mimics many aspects of cellular behavior such as cell growth, division, apoptosis and polarization. The model allows for investigation of the biomechanical properties of cells, cellcell interactions, effect of environment on cellular clusters, and how individual cells work together and contribute to the structure and function of a particular tissue. To evaluate the current approach in modeling different topologies of growing tissues in distinct biochemical conditions of the surrounding media, we model several key cellular phenomena, namely monolayer cell culture, effects of adhesion intensity, growth of epithelial cell through interaction with extracellular matrix (ECM), effects of a gap in the ECM, tensegrity and tissue morphogenesis and formation of hollow epithelial acini. The proposed computational model enables one to isolate the effects of biomechanical properties of individual cells and the communication between cells and their microenvironment while simultaneously allowing for the formation of clusters or sheets of cells that act together as one complex tissue.=The design of vector secondorder linear systems for accurate proportional damping approximation is addressed. For this purpose an error system is defined using the difference between the generalized coordinates of the nonproportionally damped system and its proportionally damped approximation in modal space. The accuracy of the approximation is characterized using the energy gain of the error system and the design problem is formulated as selecting parameters of the nonproportionally damped system to ensure that this gain is sufficiently small. An efficient algorithm that combines linear matrix inequalities and simultaneous perturbation stochastic approximation is developed to solve the problem and examples of its application to tensegrity structures design are presented. (C) 2010 Elsevier Ltd. All rights reserved.5Supramolecular assembly is a powerful strategy used by nature to build nanoscale architectures with predefined sizes and shapes. With synthetic systems, however, numerous challenges remain to be solved before precise control over the synthesis, folding and assembly of rationally designed threedimensional nanoobjects made of RNA can be achieved. Here, using the transfer RNA molecule as a structural building block, we report the design, efficient synthesis and structural characterization of stable, modular threedimensional particles adopting the polyhedral geometry of a nonuniform square antiprism. The spatial control within the final architecture allows the precise positioning and encapsulation of proteins. This work demonstrates that a remarkable degree of structural control can be achieved with RNA structural motifs for the construction of thermostable threedimensional nanoarchitectures that do not rely on helix bundles or tensegrity. RNA threedimensional particles could potentially be used as carriers or scaffolds in nanomedicine and synthetic biology.A numerical method is presented for initial selfstress design of tensegrity grid structures with exostresses. which is defined as a linear combination of the coefficients of independent selfstress modes. A discussion on proper division of the number of member groups for the purpose of existence of a single integral feasible selfstress mode has been explicitly given. Dummy elements to transform the tensegrity grid structure with statically indeterminate supports into selfstressed pinjointed system without supports are employed. The unilateral properties of the stresses in cables and struts are taken into account. Evaluation of the stability for the structure is also considered. Several numerical examples are presented to demonstrate the efficiency and robustness in searching initial single integral feasible selfstress mode for tensegrity grid structures. (C) 2010 Elsevier Ltd. All rights reserved.yThe effects of a high magnetic gradient environment (HMGE) on the cytoskeletal architecture and genes associated with the cytoskeleton in osteoblasts (MC3T3EI and MG63 cells) were investigated using confocal microscopy, realtime polymerase chain reaction (PCR) and atomic force microscopy (AFM). The findings showed that, under diamagnetic levitation c< onditions, the architecture and average height of the cytoskeleton and surface roughness in osteoblasts were dramatically altered. HMGE affects cytoskeleton arrangement and cytoskeletonassociated gene expression. (C) 2010 COSPAR. Published by Elsevier Ltd. All rights reserved.
Purpose: Prior structural studies of posterior subcapsular cataract (PSC) development in Royal College of Surgeons (RCS) rats suggest that migration of basal fiber ends was disrupted, ultimately resulting in a PSC. Therefore the goal of this study was to assess the overall migration patterns as well as changes to the structure and cytoskeleton of basal fiber ends during PSC development. Methods: Lenses from 48 RCS dystrophic rats (RCS/Lav) and 24 genetically matched control animals (RCSrdy(+)/Lav) from 2 to 8 weeks old were examined. Equatorial diameters were measured and suture patterns were photographed immediately following enucleation/dissection. Right eye lenses were fixed and processed to visualize the actin cytoskeleton via laser scanning confocal microcopy (LSCM), left eye lenses were decapsulated, fixed and processed for scanning electron microscopy (SEM). Scaled 3Dcomputer assisted drawings (CADs) and animations were constructed from the data to depict the changes in suture patterns and fiber end architecture. Results: At 2 weeks, dystrophic lenses displayed an inverted Y suture on the posterior, and by 3 weeks most lenses had at least one subbranch. Additional subbranches were observed with time, opacities being visible as early as 4 weeks and progressing into PSC plaques by 6 weeks. Control lenses displayed inverted Y sutures at all ages and were transparent. SEM of dystrophic lenses revealed fiber ends with normal size, shape, arrangement, and filopodia at 2 weeks; scattered areas of domeshaped fiber ends and small filopodia were present at 3 weeks. At 4 weeks the irregularly arranged domed fiber ends had extremely long filopodia with 'boutons' at their tips. By 6 weeks all fiber ends within plaques displayed rounded or domed basal membranes and lacked filopodial extensions. Control lenses at all time points had comparable ultrastructure to the 2 week old dystrophic lenses. Factin arrangement within the basal membrane complex (BMC) of control lenses showed the expected peripheral pattern of labeling at all ages. Dystrophic RCS lenses at 2 weeks were comparable to controls, however by 34 weeks they displayed scattered foci of Factin within the BMC. At all time points thereafter, Factin was rearranged into a 'rosette' pattern of prominent foci at cell vertices. Conclusions: The data are consistent with the hypothesis that migration of basal fiber ends is altered in a two stage process wherein initially, migration patterns undergo a rapid shift resulting in abnormal suture subbranch formation. Subsequent cytological alterations are consistent with an eventual cessation of migration, precluding proper targeting of basal ends to their sutural destinations and leading to cataract plaque formation.Determining how forces are produced by and propagated through the cytoskeleton (CSK) of the cell is of great interest as dynamic processes of the CSK are intimately correlated with many molecular signaling pathways. We are presenting a novel approach for integrating measurements on cell elasticity, transcellular force propagation, and cellular force generation to obtain a comprehensive description of dynamic and mechanical properties of the CSK under force loading. This approach uses a combination of scanning force microscopy (SFM) and Total Internal Reflection Fluorescence (TIRF) microscopy. We apply welldefined loading schemes onto the apical cell membrane of fibroblasts using the SFM and simultaneously use TIRF microscopy to image the topography of the basal cell membrane. The locally distinct changes of shape and depth of the cytoskeletal imprints onto the basal membrane are interpreted as results of force propagation through the cytoplasm. This observation provides evidence for the tensegrity model and demonstrates the usefulness of our approach that does not depend on potentially disturbing marker compounds. We confirm that the actin network greatly determines cell stiffness and represents the substrate that mediates force transduction through the cytoplasm of the cell. The latter is an essential feature of tensegrity. Most importantly, our new finding that, both intact actin and microtubule networks are required for enabling the cell to produce work, can only be understood within the framework of the tensegrity model. We also provide, for the first time, a direct measurement of the cell's mechanical power output under compression at two femtowatts. (C) 2010 WileyLiss, Inc&Nephrogenic systemic fibrosis (NSF) is a rare gadoliniumdependent disorder of the skin and viscera. The aim of this study was to revisit some immunopathologic clues of NSF, including the characterization of glycosaminoglycans, cell tensegrity, and cell proliferation in the dermis. Immunohistochemistry was done using antibodies directed to vimentin, CD34, Factor XIIIa, calprotectin, alphasmooth muscle actin, Ulex europaeus agglutinin1 (UEA1), and MIB1/Ki67 and to glycosaminoglycans, including CD44 var3, versican, and perlecan. The vimentin+ cell density was markedly increased. The vast majority of them corresponded to CD34+ or Factor XIIIa+ dermal dendrocytes (DD) showing distinct cell tensegrity. CD34+ DD were slender, elongated, and usually scattered in the dermis but focally clustered in nodular collections. By contrast, Factor XIIIa+ was plump with squat dendrites showing no evidence for being under mechanical stress. Cells in the vicinity of the microvasculature were rounded and exhibited calprotectin immunoreactivity typical for monocyte/macrophages. The microvasculature highlighted by UEA1 and alphasmooth muscle actin looked unremarkable. The cell proliferation highlighted by the MIB/Ki67 immunoreactivity was unusually high (> 20%) in the interstitial stromal cells. Stromal cells enriched in versican were plump, abundant, and seemed interconnected each other by a dense network of dendrites. By contrast, the immunolabeling for perlecan and CD44 var 3 was unremarkable. In conclusion, the cell population involved in NSF seemed phenotypically heterogeneous, and its growth fraction was clearly boosted in the skin. The intracellular load in versican was prominent. The aspect of cell tensegrity did not suggest the influence of mechanical stress putting stromal cells under tension in the dermis.Contributions from the emerging fields of molecular genetics and evodevo (evolutionary developmental biology) are greatly benefiting the field of evolutionary computation, initiating a promise of renewal in the traditional methodology. While direct encoding has constituted a dominant paradigm, indirect ways to encode the solutions have been reported, yet little attention has been paid to the benefits of the proposed methods to real problems. In this work, we study the biological properties that emerge by means of using indirect encodings in the context of formfinding problems. A novel indirect encoding model for artificial development has been defined and applied to an engineering structuraldesign problem, specifically to the discovery of tensegrity structures. This model has been compared with a direct encoding scheme. While the direct encoding performs similarly well to the proposed method, indirectbased results typically outperform the directbased results in aspects not directly linked to the nature of the problem itself, but to the emergence of properties found in biological organisms, like organicity, generalization capacity, or modularity aspects which are highly valuable in engineering. (C) 2010 Elsevier Ireland Ltd. All rights reserved.To identify the forces that may exist in the parabronchus of the avian lung and that which may explain the reported strengths of the terminal respiratory units, the air capillaries and the blood capillaries, the arrangement of the parabronchial collagen fibers (CF) of the lung of the domestic fowl, Gallus gallus variant domesticus was investigated by discri< minatory staining, selective alkali digestion, and vascular casting followed by alkali digestion. On the luminal circumference, the atrial and the infundibular CF are directly connected to the smooth muscle fibers and the elastic tissue fibers. The CF in this part of the parabronchus form the internal column (the axial scaffold), whereas the CF in the interparabronchial septa and those associated with the walls of the interparabronchial blood vessels form the external, i.e. the peripheral, parabronchial CF scaffold. Thin CF penetrate the exchange tissue directly from the interparabronchial septa and indirectly by accompanying the intraparabronchial blood vessels. Forming a dense network that supports the air and blood capillaries, the CF weave through the exchange tissue. The exchange tissue, specifically the air and blood capillaries, is effectively suspended between CF pillars by an intricate system of thin CF, elastic and smooth muscle fibers. The CF course through the basement membranes of the walls of the blood and air capillaries. Based on the architecture of the smooth muscle fibers, the CF, the elastic muscle fibers, and structures like the interparabronchial septa and their associated blood vessels, it is envisaged that dynamic tensional, resistive, and compressive forces exist in the parabronchus, forming a tensegrity (tension integrity) system that gives the lung rigidity while strengthening the air and blood capillaries."The main objective of this paper is twofold. First, to conclude the overview about tensegrity frameworks, started by the same authors in a previous work, covering the most important dynamic aspects of such structures. Here, the most common approaches to tensegrity dynamic modeling used so far are presented, giving the most important results about their dynamic behavior under external action. Also, the main underlying problems are identified which allow the authors to give a clear picture of the main research lines currently open, as well as the most relevant contributions in each of them, which is in fact the second main objective of this paper. From the extensive literature available on the subject, four main areas have been identified: design and formfinding methods which deal with the problem of finding stable configurations, shape changing algorithms which deal with the problem of finding stable trajectories between them and, also control algorithms which take into account the dynamic model of the tensegrity structure and possible external perturbations to achieve the desired goal and performance. Finally, some applications of such structures are presented emphasizing the increasing interest of the scientific community on tensegrity structures. (C) 2008 Elsevier Ltd. All rights reserved.CThe development of tensegrity mechanisms is motivated by their reduced inertia which is made possible by an extensive use of cables and springs. In this paper, a new spatial tensegrity mechanism is introduced. The direct and inverse static problems of the mechanism are solved by minimizing its potential energy. For a simplified case where external and gravitational loads are neglected, analytical solutions to these problems are found and are then used to compute the boundaries of the mechanism's actuator and Cartesian workspaces. (C) 2008 Elsevier Ltd. All rights reserved.fThis paper presents a simple and efficient method to determine the selfequilibrated configurations of prismatic tensegrity structures, nodes and members of which have dihedral symmetry. It is demonstrated that stability of this class of structures is not only directly related to the connectivity of members, but is also sensitive to their geometry (height/radius ratio), and is also dependent on the level of selfstress and stiffness of members. A catalogue of the structures with relatively small number of members is presented based on the stability investigations. (c) 2008 Elsevier Ltd. All rights reserved.?The design of structures for dynamic properties is addressed by placing conditions on the separation between natural frequencies. Additional constraints, like lower and upper bounds on the natural frequencies, are also included. A fast numerical algorithm that exploits the mathematical structure of the resulting problem is developed. Examples of the algorithm's application to tensegrity structures design are presented and the connection between natural frequencies separation and proportional damping approximation is analyzed. (C) 2008 Elsevier Ltd. All rights reserved.This paper addresses the issues of control and workspace determination of planar active tensegrity or tensegritylike structures. The motion of such structures is generally produced by actuated cables, which cannot tolerate compressive forces. Hence, a controller which not only satisfies the system dynamic equations, but also maintains positive tension in cables is necessary. A nullspace controller based on feedback linearization theory is developed for this purpose. This controller utilizes redundant active cables to overactuate the system. The concept of a 'dynamic workspace' for these structures is then introduced. This workspace consists of all configurations that are achievable from a given initial configuration while maintaining positive tensions throughout the entire system motion and is a powerful tool in analyzing the performance of a variety of tensegrity structures. This idea extends the concept of the static workspace, which consists of statically maintainable configurations, by incorporating system motion and dynamics to guarantee positive tensions during transition between the states. A critical benefit of this procedure is that it may be used to find the dynamic workspace of a system regardless of whether actuator redundancy is utilized, and thus can be used to objectively illustrate the degree to which overactuation improves mobility of a tensegrity structure. The effectiveness of the developed concepts is demonstrated through computer simulation and actual physical experimentation./This paper presents a general method to perform the stiffness analysis of tensegrity mechanisms. The method is based on an existing stiffness matrix model. Several stiffness indices having physical meaning are introduced As an example, the method is applied to a planar 2DoF tensegrity mechanism. Stiffness mappings based on the stiffness indices are generated for the mechanism's workspace. It is shown for the example mechanism that the effect of the prestress on the stiffness is not significant when linear stiffness models of the components are assumed.$Tensegrities consist of disjoint struts connected by tensile strings which maintain shape due to prestress stability. Because of their rigidity, foldability and deployability, tensegrities are becoming increasingly popular in engineering. Unfortunately few effective analytical methods for discovering tensegrity geometries exist. We introduce an evolutionary algorithm which produces large tensegrity structures, and demonstrate its efficacy and scalability relative to previous methods. A generative representation allows the discovery of underlying structural patterns. These techniques have produced the largest and most complex irregular tensegrities known in the field, paving the way toward novel solutions ranging from space antennas to soft robotics. (C) 2008 Elsevier Ltd. All rights reserved.GSingularity theory is applied for the study of constrained tensegrity systems. Previous studies have already been performed on nonconstrained systems; however, the present one allows for general nonsymmetric equilibrium configurations. A modified T3 tensegrity model comprising seven rigid bars, three elastic cables and one rotational spring is considered. The stability of this model is examined performing singularity theory for deformations under conservative quasistatic loading. Critical conditions for branching of the equilibrium paths are defined and their postcritical behavior is discussed. Classification of the simple and compound singularities of the total potential energy function is effected. The theory is implemented into the fold catastrophe of the as< ymmetric configuration of the modified T3 tensegrity model and an elliptic umbilic singularity for the case of compound branching. It is pointed out that singularity studies with constraints demand a quite different mathematical approach than those without constraints. (C) 2009 WILEYVCH Verlag GmbH & Co. KGaA, Weinheim;This paper presents: the tensegrity concept applied to inorganic matter (the construction of the "buckyball" model for water; the tensegrity icosahedron for the hexagonal model of water); a review of the natural tensegrity forms found in living life, from micro to macro level and the different tensegrities which approximate them, including some realisations of the members of the scientific association Methodology of technical sciences teaching, from the Faculty of Mechanics, University of Craiova; new trends towards optimally designing mechanisms and mobile robots.This paper presents a lowcost experimental technique to carry out damage assessment of structures using dynamic strain measured by of surfacebonded piezo transducers. The technique is applied on a single module tensegrity structure, 1mx1m in size and then extended to a tensegrity grid structure, 2mx2m size, fabricated using galvanised iron (GI) pipes and mild steel cables. A single piezoelectricceramic (PZT) patch bonded on a strut measures the dynamic strain during an impact excitation of the structure. Damage is identified from the frequency response function (FRF) obtained after domain transformation of the PZT patch's response. For the grid structure, damage is localized using changes in the three natural frequencies observed experimentally and the corresponding mode shapes obtained numerically. The technique is found to be very expedient and at the same time cost effective, especially for preliminary damage detection in the structures.We present proofs of two classical theorems. The first one, due to Darboux and Sauer, states that infinitesimal rigidity is a projective invariant; the second one establishes relations (infinitesimal Pogorelov maps) between the infinitesimal motions of a Euclidean framework and of its hyperbolic and spherical images. The arguments use the static formulation of infinitesimal rigidity. The duality between statics and kinematics is established through the principles of virtual work. A geometric approach to statics, due essentially to Grassmann, makes both theorems straightforward. Besides, it provides a simple derivation of the formulas both for the DarbouxSauer correspondence and for the infinitesimal Pogorelov maps.In this paper we report development of three dimensional silicon microenvironments in order to test the morphological changes and adhesion properties of human breast cancer cells after treatment with different anticancer drugs such as Trichostatin A (TSA), suberoylanilide hydroxamic acid (SAHA) and Scriptaid. Our results indicate that the cancer cells reorganize their cytoskeleton structure after treatment with TSA and Scriptaid. However, SAHA does not change the behavior of the cells inside the three dimensional microstructures while TSA and Scriptaid evoked striking changes in the cells morphology. TSA and Scriptaid drugs cause the cells to stretch inside the
!"#$%&'()*+,./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcefghijklmnopqrstuvwxyz{}~isotropic microchambers to avoid contact with curved sidewalls in contrast to their originally rounded shape. The proposed microstructures can be used to evaluate mechanical properties and the pathological grade of various cancer cell lines after different conditions i.e. drug exposure.Tensegrity structures can provide a new approach to the construction of mobile robots with different shapes and properties that usual robots, wheeled or legged, do not have. Tensegrity are light, deformable structures that may be able to adapt their form to unconstrained environments. The main issue of this paper is twofold, first, to derive appropriate and general dynamic equations of motion to study the movement of such structures in the space; second to demonstrate, by means Of simulation, that a tensegrity structure can execute any desired trajectory path by actuating some or all of its elements. (c) 2008 Elsevier B.V. All rights reserved.KRhythmic movements associated with animal locomotion are controlled by neuronal circuits known as central pattern generators (CPG). These biological control systems appear to entrain to the natural frequencies of the mechanical systems they control, taking advantage of the resonance of the structure, resulting in efficient control. The ultimate goal is employing these controls in a biomimetic autonomous underwater vehicle so as to capture, and possibly improve upon, the performance capabilities of animals like the manta ray. To this end, this paper investigates the CPG control of a simple tensegrity structure. The dynamics of a tensegrity structure are linearized about a nominal configuration, and a synthesized CPG is used as the control input. Successful integration is shown by the CPG's ability to tune the structure's first mode.We study characterizations of generic rigid graphs and generic circuits in the plane using only few decompositions into spanning trees. Generic rigid graphs in the plane can be characterized by spanning tree decompositions [5,6]. A graph G with n vertices and 2n3 edges is generic rigid in the plane if and only if doubling any edge results in a graph which is the union of two spanning trees. This requires 2n3 decompositions into spanning trees. We show that n2 decompositions suffice: only edges of GT can be doubled where T is a spanning tree of G. A recent result on tensegrity frameworks by Recski [7] implies a characterization of generic circuits in the plane. A graph G with n vertices and 2n2 edges is a generic circuit in the plane if and only if replacing any edge of G by any (possibly new) edge results in a graph which is the union of two spanning trees. This requires (2n2)((n/2)1) + 1 decompositions into spanning trees. We show that 2n2 decompositions suffice. Let e(1), e(2), ... , e(2n2) be any circular order of edges of G (i.e. e(0) = e(2n2)). The graph G is a generic circuit in the plane if and only if G + e(i)  e(i1) is the union of two spanning trees for any i = 1, 2, ... , 2n2. Furthermore, we show that only n decompositions into spanning trees suffice.^This paper presents a novel formfinding algorithm for tensegrity structures that is based on the finite element method. The required data for the formfinding is the topology of the structure, undeformed bar lengths, total cable length, prestress of cables and stiffness of bars. The formfinding is done by modifying the single cable lengths such that the total cable length is preserved and the potential energy of the system is minimized. Two and threedimensional examples are presented that demonstrate the excellent performance of the proposed algorithm. (C) 2009 Elsevier Ltd. All rights reserved.dAs tensegrity research is moving away from static structures toward active structures it is becoming critical that new actuation strategies and comprehensive active structures theories are developed to fully exploit the properties of tensegrity structures. In this paper a new general tensegrity paradigm is presented that incorporates a concept referred to as clustered actuation. Clustered actuation exploits the existence of cable elements in a tensegrity structure by allowing cables to be run over frictionless pulleys or through frictionless loops at the nodes. This actuation strategy is a scalable solution that can be utilized for active structures that incorporate many active elements and can reduce the number of actuators necessary for complex shape changes. Clustered actuation also has secondary benefits, specifically reducing the force requirements of actuators in dynamic structures, reducing the number of prestress modes to potentially one global mode and relieving element size limitations that occur with embedded actuation. Newly formulated clustered equilibrium equations are developed using energy methods and are shown to be a generalization of the classic tensegrity governing equations. Prestress analysis, mechanism analysis and stability< of clustered structures are discussed. Lastly, examples compare the mechanics of a clustered structure to an equivalent classic structure and the utility of clustering is highlighted by allowing for actuation throughout a class 1 (no bartobar connections) tensegrity while not embedding the actuators into the structure. (C) 2009 Elsevier Ltd. All rights reserved.The logarithmic strain measure is used to obtain a consistent geometric nonlinear finite element formulation to deal with large strains on space trusses. The formulation is based on the positional formulation and no local system of coordinates on the elements is needed to describe its kinematics. Three numerical examples are presented, including a tensegrity tower and a double layer elastoplastic space truss. The paper proves that the positional nonlinear formulation is valid for other objective strain measures used in the classical nonlinear formulations, i.e. logarithmic strain measure. (c) 2009 Elsevier B.V. All rights reserved.{The goal of this work is to stabilize the shape and orientation of formations of N identical and fully actuated agents, each governed by doubleintegrator dynamics. Using stability and rigidity properties inherent to tensegrity structures, we first design a tensegritybased, globally exponentially stable control law in one dimension. This stabilizes given interagent spacing along the line, thereby enabling shape control of onedimensional formations. We then couple onedimensional control laws along independent orthogonal axes to design a distributed control law capable of stabilizing arbitrary shapes and orientations in n dimensions. We also present two methods for formation shape and orientation change, one using smooth parameter variations of the control law, and the other, an nstep collisionfree algorithm for shape change between any two formations in ndimensional space.Key properties of tensegrity structures are reviewed and illustrated on a representative structure. These properties reveal an ideal way of motion using infinitesimal internal mechanisms. Consequently, a new motion control strategy which exploits these mechanisms is introduced.This chapter traces down the roots of the first manmade objects which resemble what are nowadays known as tensegrity structures. It then shows how the tensegrity concept evolved, finding increasingly large audience in engineering, mathematics, and biology. The history of tensegrity structures research is presented including references to the most important discoveries and examples of the author's contributions. Some of the current challenges these structures face in the area of practical applications conclude the chapter.#Tensegrity frameworks are defined on a set of points in Rd and consist of bars, cables, and struts, which provide tipper and/or lower bounds for the distance between their endpoints. The graph of the framework, in which edges are labeled as bars, cables, and struts. is called a tensegrity graph. It is said to be rigid in Rd if it has an infinitesimally rigid realization in Rd as a tensegrity framework. The characterization of rigid tensegrity graphs is not known for d >= 2. A related problem is how to find a rigid labeling of a graph using no bars. Our main result is an efficient combinatorial algorithm for finding a rigid cablestrut labeling of a given graph in the case when d 2. The algorithm is based on a new inductive construction of redundant graphs, i.e. graphs which have a realization as a bar framework in which each bar can be deleted without increasing the degree of freedom. The labeling is constructed recursively by using labeled versions of some wellknown operations on bar frameworks. (C) 2008 Elsevier Ltd. All rights reserved.In this paper, a threemember tensegrity structure is used as a conceptual model for the dendritic actin network in living cells. The pre and postbuckling behavior of the tensegrity is analyzed basing on the energy method. Analytical simulations are carried out on the tensegrity by using the experimentally obtained scales and mechanic properties of actinfilaments for the structural members of the tensegrity. The model exhibits a stress stiffening regime followed by a stress softening regime in the loadstiffness relationship, which qualitatively tallies with the experimentally observed response of actin networks. Due to the simplicity of the model, there is only a single compressed member and the structure buckles abruptly, which results a softening regime much steeper than that observed in the actin network. To take the member length variety into account, we propose a conceptual largescale tensegrity system with various member lengths, and its behavior is approximately estimated by the mean response of a large number of threemember tensegrity cells with their member length varying in the range of filament lengths. The obtained mean response exhibits a much better fitness to the response of actin networks than those exhibited by the single tensegrity model. The findings reported in this paper indicate that the dendritic actin network may work as a complex tensegrity system, when it is subjected to a stress.The development of the "non standard" architecture, mainly based on curved surfaces using rigid frames combined with cladding panels, emphasizes on new needs. A lightweight innovative solution has been developed to provide adaptable flat or curved cladding panels fixed on the supporting structure, with thermal insulation and possible prefabrication. The panels are realized with an association of tensile membranes and a woven structure of prestressed composite profiles. They are designed on the principle of tensegrity and provide both properties of flexibility and rigidity. Mechanical studies have been performed to determine the relationships between the panel shape and its initial stresses ("form control" and "force control" strategies) and a FEM analysis allows identifying the behavior in association with experimental testing on a prototype system. In parallel, thermal studies have been initiated to evaluate the performance of this double membrane panel.The shapes of the prestressed cable structures are sensitive to external errors/stimuli due to their lightweight and high flexibility. When the shape distortion is deemed unacceptable, adjustment of the nodal positions is needed. For structures of linear behaviour, the displacement control problem can be converted to an optimization question. Simulated annealing algorithm combined with a technique derived from linear force method is implemented to solve this optimization question. And then, based on the linear displacement control technique and the nonlinear force method, an iteration procedure is proposed to achieve the nonlinear displacement control of prestressed cable structures. Two numerical examples are conducted which show that the computational results of the nonlinear control method are in well agreement with the target values, while there are considerable errors for the corresponding results of the linear control method.We study the possibility to use the measurement of the displacement fields of the nodes of a tensegrity structure under static loading to obtain a new method for the identification of its selfstress state. We try to determinate the correlation between the precision of this identification and the precision of the measure. With a tacheometer we obtain a precision of identification as good as the standard method using efforts measurements.%In this paper, we describe the design of a deformable robot with a tensegrity structure that can crawl and we show the results of experiments showing the ability of these robots to crawl. We first describe a tensegrity structure, composed of struts and cables, and its characteristics. We next explain the principle of crawling by robot body deformation, followed by a classification of the methods by which a body can be deformed and the contact conditions of the robot through the cablegraph of the tensegrity structure. We also describe topological transition graphs that can visualize crawling from each initial contact condition. We t< hen discuss the characteristics of the proposed robot in terms of design freedom. Finally, we show experimentally that the prototype of a tensegrity robot can crawl.The threedimensional finite element (FE) model of eucaryotic cell presented in the paper is based on similar models published recently; it comprehends elements representing cell membrane, cytoplasm and nucleus, and a complex tensegrity structure representing cytoskeleton. In contrast to the previous models, this tensegrity structure consists of several parts. External and internal parts count 30 struts and 60 cables each and their corresponding nodes are interconnected by 30 radial members; these parts represent cortical, nuclear and deep cytoskeletons, respectively. This arrangement enables us to simulate the load transmission from the extracellular space via membrane receptors (focal adhesions) to the central part of the cell (nucleus, centrosome); this ability of the model was tested by simulation of some mechanical tests of isolated cells, in particular tension test with micropipettes, indentation test and magnetic tweezer test. Although material properties of components have been defined as realistic as possible on the base of the mechanical tests with vascular smooth muscle cells, they were not identified in fact and are not unique probably. However, simulations of the tests have shown the ability of the model to simulate the global loaddeformation response of the cell under various types of loadings, as well as several substantial global features of the cell behaviour, e.g. "at a distance effect", nonlinear stiffening with increasing load, or linear dependence of stiffness on increasing prestrain.The stability of space reticulate systems is dependent on the existence of mechanisms. The methods that have been developed to determine them are mainly based on the calculation of a basis of the mechanisms' vectorial subspace by computing the kernel of the transpose equilibrium matrix of the structure. However, they can only consider a bilateral stiffness of the members, which applies to the case for systems composed of bars with traction and compression stiffness. Nevertheless, some classes of reticulate systems, like tensegrity systems, use unilateral rigidity components such as cables. The objective of this paper is to develop a method for calculating the mechanisms which can take into consideration the presence of components with unilateral rigidity. In this case, specific mechanisms associated with these elements may appear; these are referred to as "unilateral mechanisms". An approach is therefore proposed in order to write a basis of their vectorial subspace. It is included in a methodology devoted to the analysis of space structures with initial stresses. The process is based on the identification of the possible prestress states and of the bilateral mechanisms and, next, to the characterization of the unilateral mechanisms. (c) 2007 Elsevier Masson SAS. All rights reserved.kThis study focuses on improving structural control through reinforcement learning. For the purposes of this study, structural control involves controlling the shape of an active tensegrity structure. Although the learning methodology employs casebased reasoning, which is often classified as supervised learning, it has evolved into reinforcement learning, since it learns from errors. Simple retrieval and adaptation functions are proposed. The retrieval function compares the response of the structure subjected to the current loading event and the attributes of cases. When the response of the structure and the case attributes are similar, this case is retrieved and adapted to the current control task. The adaptation function takes into account the control quality that has been achieved by the retrieved command in order to improve subsequent commands. The algorithm provides two types of learning: reduction of control command computation time and increase of control command quality over retrieved cases. Results from experimental testing on a fullscale active tensegrity structure are presented to validate performance.The formation of DNAbased nanostructures involves the binding of different kinds of ligands to DNA as well as the interaction of DNA molecules with each other. Complex formation between ligand and DNA can alter physicochemical properties of the DNA molecule. In the present work, the accessibility of DNAligand complexes to cleavage by DNase I are considered, and the exact algorithms for analysis of diagrams of DNase I footprinting for ligandDNA complexes are obtained. Changes of mechanical properties of the DNA upon ligand binding are also demonstrated by the cleavage patterns generated upon ultrasound irradiation of cisplatinDNA complexes. Propagation of the mechanical perturbations along DNA in the presence of bound ligands is considered in terms of a string model with a heterogeneity corresponding to the position of a bound ligand on DNA. This model can reproduce qualitatively the cleavage patterns obtained upon ultrasound irradiation of cisplatinDNA complexes.The first part of this paper extends the pioneering work of Kenneth Snelson on tensegrity towers. The generalized method is capable of producing towers and arches with any number of bars at each level. Examples of towers with four, seven and ten bars at each level are presented. An arch is constructed based on the same concept. Also a cablestayed bridge with two tensegrity arches is proposed. The second part of the paper presents a method for generating tensegrity roofs for stadiums. A hexagonal tensegrity cell is proposed as the basic building block for creating roofs of arbitrary geometries. Various computer generated models and physical models are presented to demonstrate the generality and applicability of the proposed methods.NOVELTY  The dense filling type tensegrity joint has coated tension portions (71), each converge into a guidance slit facing across a cylindrical tunnel. A spherical caulking material (61) is stabilized on the bottom face of the cylindrical tunnel. USE  Dense filling type tensegrity joint tensegrity structure (claimed). Can also be used for structural system for film membrane structure, accurate and economical research educational model and large sized tent. ADVANTAGE  The compressive stress by external force, can be distributed in an efficient manner. The need of mechanical fastening, is eliminated. The time of assembly of tensegrity structure, is reduced. The discontinuous arrangement in a threedimensional space, is enabled.This paper hands in a review of the basic issues about the statics of tensegrity structures. Definitions and notation for the most important concepts, borrowed from the vast existing literature, are summarized. All of these concepts and definitions provide a complete mathematical framework to analyze the rigidity and stability properties of tensegrity structures from three different, but related, points of view: motions, forces and energy approaches. Several rigidity and stability definitions are presented in this paper and hierarchically ordered, from the strongest condition of infinitesimal rigidity to the more wide concept of simple rigidity, so extending some previous classifications already available. Important theorems regarding the relationship between these definitions are also put together to complete the static overview of tensegrity structures. Examples of different tensegrity structures belonging to each of the rigidity and stability categories presented are described and analyzed. Concluding the static analysis of tensegrity structures, a review of existing formfinding methods is presented. (C) 2007 Elsevier Ltd. All rights reserved. Research on cylindrical and spherical tensegrity modules are extensively carried out. However research on other tensegrity modules is little reported. This paper presents an exploratory study on a new kind of tensegrity module  "torus". The topology of the torus tensegrity is firstly introduced. Then the initial formfinding of the torus tensegrity is discussed. The static and dynamic analysis of the torus tensegrity shows that pre< stressing has a stiffening effect on infinitesimal mechanism modes if the geometry is properly arranged. A new cable dome with a torus tensegrity employed as its ring beam is finally proposed. The behavior of the new dome is also examined. The work here will provide a reference for further research and application of the torus tensegrity.Tensegrity systems are structures in equilibrium under an initial selfstress state. This selfstress state is composed of elementary selfstress states, which constitute its basis. They have complex behaviour and the selfstress state can be modified by external loads. A continuous dialogue between numerical simulations and experimental tests made it possible to validate previous models. In this paper, we checked the validity of the indirect methods currently used to measure cable tension. Static and vibratory measurements clearly show that the bending moment of the elements influences the behaviour of the structure. In the computational analysis, it is therefore necessary to consider embedding of the elements although the structure is not entirely rigid. Moreover, structural beam finite elements are necessary for a correct calculation of bar behaviour within the structure. Our results contribute to improve the modelling of the behaviour of tensegrity grids as conceived in the Tensarch project. (c) 2007 Elsevier Ltd. All rights reserved.Many different robotic inparallel structures have been conceived as sixcomponent force sensors. In general, they perform well for most applications but, when accuracy is a must, two main limitations arise. First, in most designs, the legs are connected to the base and the platform through ballandsocket joints. Although the dry friction in each of these joints can be individually neglected, the integrated effect of twelve such elements becomes noticeable. Second, dynamical measurements might not be very accurate because the natural resonance frequency of the used structures is quite low even for relatively small dimensions. This dynamical response can be obviously modified with a proper mechanical design, but this increases the complexity of the sensor. This paper discusses the design and implementation of a touch pad based on a 6axis force sensor and shows how the above limitations degrade its behavior. Moreover, it is shown how using a tensegrity structure both problems could be alleviated because ballandsocket joints can be substituted by point contacts and the resonance frequency of the structure can be controlled by adjusting the static tensions of the tendons.In this paper we propose a new framework for deformation modelling based on a combined mass spring and tensional integrity method. The synergy between balanced tension and compression components offered by the tensegrity model helps the deforming organ retain its shape more consistently. We chose the diaphragm as our test object given its heterogeneous composition (muscle and tendon) and its importance in radiotherapy and other interventional procedures. Diaphragm motion can significantly influence surrounding organs such as lungs and liver. Our system permits the control of simulated diaphragm motion and deformation by at least two independent parameters.This paper presents the experimental analysis of a tensegrity structure based on truncated icosahedron geometry. The objective of the study is to characterize the mechanical behavior of a tensegrity dome. Two reduced scale tensegrity domes were assembled, one of which was instrumented for the laboratory experiments. The experimental data collected are related with structural displacements, strain in the bars and strain in the cables. (c) 2008 Elsevier Ltd. All rights reserved.Tensegrity mechanisms benefit from a reduced inertia due to their extensive use of cables and springs. However, they must be prestressed at all times in order to keep the cables in tension. For a given mechanism architecture, this is only possible in a specific set of configurations such that the analysis of these mechanisms is relatively complex. This paper presents the development and analysis of a new threedegreeoffreedom positional tensegrity mechanism that has a modular architecture. The mechanism, actuated by cables, has a relatively large workspace. For the special case where external and gravitational forces are neglected, solutions are given for the mechanism's equilibrium configuration both for given actuator positions as well as for a specified position of its effector. It is shown that the mechanism can be considered as an assembly of construction elements based on Snelson's Xshape tensegrity system and that these behave independently from one another.zThe paper considers issues of creating loadcarrying systems whose failure occurs gradually under onepath or repeatedly variable quasistatic loadings, which enables to prevent a failure. Due to loadings of certain classes such systems have uprated strength, rigidity and safety, and therefore are called geometrically strengthening systems. Indicated structural features are found exactly with allowance for geometrical nonlinearity. Material deforming diagrams can be nonmonotonic and nonsmooth, and constraints can be unilateral, with gaps. The optimization mathematic models of structures as discrete mechanical systems withstanding monotonic or cyclic static and kinematic actions are proposed. To find limit parameters of these actions the extreme energetic principle is suggested what result in the nonlinear mathematic programming problem statement. Here is given a set of known and new criteria for plastic yielding stability of structures, including for nonsmooth and nonconvex problems of optimization. In the paper an example of using the proposed methods is presented and geometrically strengthening system is taken into account.PThis paper presents a closedform analysis of a series of planar tensegrity structures to determine all possible equilibrium configurations for each device when no external forces or moments are applied. The equilibrium position is determined by identifying the configurations at which the potential energy stored in the springs is a minimum. The degree of complexity associated with the solution was far greater than expected. For a twospring system, a 28th degree polynomial expressed in terms of the length of one of the springs is developed where this polynomial identifies the cases where the change in potential energy with respect to an infinitesimal change in the spring length is zero. Three and four spring systems are also analyzed. These more complex systems were solved using the Continuation Method. Numerical examples are presented.oin this paper the kinematic and the dynamic analysis, and a nonlinear control strategy for a planar threedegreeoffreedom tensegrity robot manipulator are addressed. A geometric method is used to obtain the set of equations that describe the position analysis. Initially, solutions to the problems concerning forward and reverse kinematic analysis are presented; then, the forward velocity coefficients matrix is obtained analytically. The Lagrangian approach is used to deduce the dynamic equation of motion and its main properties are described using the nonlinear control system theory. Finally, a feedbacklinearizationbased nonlinear control scheme is applied to the mechanism to follow a prescribed path in the Cartesian coordinate system. The obtained results show that lightweight mechanisms which incorporate tensegrity systems could be used in a positioning problem.Tensegrity mechanisms are selfstressing mechanisms and it is known that the prestress of the elements affect the stiffness of the tensegrity In this paper stiffness of a spatial tensegrity is studied for the purpose of the noise and vibration control and it is shown that an efficient variable stiffness element can be designed by using tensegrities. The antagonistic force and antagonistic stiffness are explained briefly and the kinematics of the tensegrity is analyzed. Also, the possible motion, the elastic stiffness, load stiffness and antagonistic stiffness formulation for the tensegrity are found symbo< lically. Some techniques for increasing the magnitude of the antagonistic stiffness are mentioned. The effect of the geometry on the stiffness, stiffness controllability and linearity are shown by examples. Finally, the results of this approach are verified by mechanical simulation of the designed tensegrity.Cellular biomechanics is an area of study that is receiving more attention as time progresses. The response of cells to their mechanical environment, including biomechanical stimuli, has farreaching rami. cations for the area of tissue engineering, especially for tissues designed to withstand mechanical loading (e. g. bone, cartilage, tendons and ligaments, and arteries). The effects of mechanical stimuli on cells are only recently being examined, and the potential role of mechanical stimuli in tissue engineering is still one that is largely ignored in the design of tissue engineering scaffolds. The relationship of mechanical properties of scaffolds or of mechanical stimuli to cell behavior is complex, but vital to the development of the field. Also, understanding the complex interplay of form and environment on cells involves an increase in our knowledge of how cells react to their total environment including mechanical stimuli and material properties. In order to improve tissue engineering outcomes, a nexus must be developed between the mechanical, biochemical, and biological studies of cellular behavior, in the context of extremely complex systems.We present a modular robot design inspired by the creation of complex structures and functions in biology via deformation. Our design is based on the Tensegrity model of cellular structure, where active filaments within the cell contract and expand to control individual cell shape, and sheets of such cells undergo largescale shape change through the cooperative action of connected cells. Such deformations play a role in many processes, e.g. early embryo shape change and lamprey locomotion. Modular robotic systems that replicate the basic deformable multicellular structure have the potential to quickly generate largescale shape change and create dynamic shapes to achieve different global functions. Based on this principle, our design includes four different modular components: (1) active links, (2) passive links, (3) surface membranes, and (4) interfacing cubes. In hardware implementation, we show several selfdeformable structures that can be generated from these components, including a selfdeformable surface, expandable cube, terrainadaptive bridge [1]. We present experiments to demonstrate that such robotic structures are able to perform real time deformation to adapt to different environments. In simulation, we show that these components can be configured into a variety of bioinspired robots, such as an amoebalike robot and a tissueinspired material. We argue that selfdeformation is wellsuited for dynamic and sensingadaptive shape change in modular robotics.Tensegrity structures appeared in the science community about half a century ago, but they have already been applied to several heterogeneous research fields, such as architecture, civil engineering, space and even biology. Such structures keep a stable volume in space due to an intricate balance of forces between a disjoint set of rigid elements (bars) and a continuous set of tensile elements (cables). The use of tensegrity structures in robotics is still new and there exist only a handful of works about this subject. Some of their main features such as light weight, flexibility, energetic efficiency and redundancy, make them interesting candidates for both mobile robots and manipulators. In this paper, a new method to detect and avoid both internal collisions between the structure members and external collisions with the environment is presented. In this way, we are providing a fundamental tool to develop more complete formfinding procedures and pathplanning strategies for tensegrity structures.In Ludwig Danzer's Habilitatiionsschrift [L. Danzer, Endliche Punktmengen auf der 2Sphare mit moglichst grossem minimalabstand, Habilitationsschrift, Gottingen, 1963] he initiated a study of the local nature of the packings from the point of view of whether their density can be increased by a small perturbation of the packing configuration. This is an abbreviated biased introduction to the theory of such locally maximally dense packings of disks in various spaces from the point of view of the theory of tensegrity structures. This has applications to jamming of granular materials as well as leading to a better understanding of jammed packings. (C) 2008 Elsevier Ltd. All rights reserved.This paper presents progress in the field of adaptive civilengineering structures. Selfdiagnosis, multiobjective shape control and reinforcementlearning processes are implemented within a control framework on an active tensegrity structure. Selfdiagnosis extends active structural control to situations of partially defined loads. Multiobjective search is useful for computing commands that control shape while minimizing active strut stroke and stress, and maximizing stiffness. Reinforcement learning improves the control by memorizing, retrieving and adapting previous control events. The control framework is validated experimentally on an active tensegrity structure. This provides an example of an adaptive civilengineering structure. (C) 2008 Elsevier Ltd. All rights reserved.This paper addresses the issues of control and workspace determination of planar active tensegrity or tensegritylike structures. The motion of such structures is generally produced by actuated cables, which cannot tolerate compressive forces. Hence, a controller, which not only satisfies the system dynamic equations but also maintains positive tension in cables, is necessary. A nullspace controller based on feedback linearization theory is developed for this purpose. This controller utilizes redundant active cables to overactuate the system. The concept of a "dynamic workspace" for these structures is then introduced. This workspace consists of all configurations that are achievable from a given initial configuration while maintaining positive tensions throughout the entire system motion, and it is a powerful tool in analyzing the performance of a variety of tensegrity structures. This idea extends the concept of the static workspace, which consists of statically maintainable configurations, by incorporating system motion and dynamics to guarantee positive tensions during transition between the states. A critical benefit of this procedure is that it may be used to find the dynamic workspace of a system regardless of whether actuator redundancy is utilized, and thus it can be used to objectively illustrate the degree to which overactuation improves mobility of a tensegrity structure. The effectiveness of the developed concepts is demonstrated through computer simulation and actual physical experimentation.This paper presents the equilibrium analysis of a planar tensegrity mechanism. The device consists of a base and top platform that are connected in parallel by one connector leg (whose length can be controlled via a prismatic joint) and two spring elements whose linear spring constants and free lengths are known. The paper presents three cases: (I) the spring free lengths are both zero, (2) one of the spring free lengths is zero and the other is nonzero. and (3) both free lengths are nonzero. The purpose of the paper is to show the increase in complexity that results from nonzero free lengths. It is shown that 6 equilibrium configurations exist for case 1. 20 equilibrium configurations exist for case 2, and 62 configurations exist for case 3.aA multiobjective search method is adapted for supporting structural control of an active tensegrity structure. Structural control is carried out by modifying the selfstress state of the structure in order to satisfy a serviceability objective and additional robustness objectives. Control commands are defined as sequences of contractions and elongations of active struts to modify the selfstress state of the structure. A two step mult< iobjective optimization method involving Pareto filtering with hierarchical selection is implemented to determine control commands. Experimental testing on a fullscale active tensegrity structure demonstrates validity of the method. In most cases, control commands are more robust when identified by a multiobjective optimization method as compared to a single objective one. This robustness leads to better control over successive loading events. Evaluation of multiple objectives provides a more global understanding of tensegrity structure behavior than any single objective. Finally, results reveal opportunities for selfadaptive structures that evolve in unknown environments.The computation of the equilibrium configurations of tensegrity mechanisms is often a very tedious task even for relatively simple architectures. However, it has been observed that the complexity of this problem is significantly reduced when gravitational loads are compensated with the use of static balancing techniques. In this work, the general static balancing conditions are adapted for the case of tensegrity mechanisms. Afterward, the modified conditions are applied to two new spatial three degree offreedom tensegrity mechanisms.This paper concludes the characterization of 3realizable graphs begun by Belk and Connelly. A graph is 3realizable if, for every configuration of its vertices in EN with N >= 3, there exists a corresponding configuration in E3 with the same edge lengths. In this paper the two graphs V8 and C5 x C2 are shown to be 3realizable. As shown by Belk and Connelly, this means that the forbidden minors for 3realizability are K5 and K2,K2,K2.During immune responses, macrophages play important roles in phagocytosis and antigen presentation by engulfing pathogenic microorganisms and cell debris. Since the function of a macrophage highly depends on a series of physical steps including migration, direct contact and strong binding to its target, deployment of cytoplasm and membrane, and intake of the target, here we have investigated the mechanical behavior of a macrophage by manipulating it with a flexible pipette that was used as a force sensor and transducer. We examined the response of a macrophage to mechanical pulling by a positively charged pipette. We observed that the macrophage initially formed strong binding to the pipette and migrated along the direction of pulling for some early period. After that period, the macrophage exerted a huge traction force to pull the pipette back and attempted to retract itself towards its original location. We found that whether it was able to return to the original location depended on the level of applied force. Since the traction force generated by a single macrophage had not been characterized accurately, we measured the force for the first time to our knowledge and found the maximum traction force to be around 80 nN. This quantitative measurement was made possible by a new and convenient method used to calibrate the stiffness of the pipette. Through the study, we acquired a better understanding of the mechanics of and the force generation by a macrophage.Current attempts to build fast, efficient, and maneuverable underwater vehicles have looked to nature for inspiration. However they have all been based on traditional propulsive techniques, i.e., rotary motors. In the current study a promising and potentially revolutionary approach is taken that overcomes the limitations of these traditional methodsmorphing structure concepts with integrated actuation and sensing. Inspiration for this work comes from the manta ray (Manta birostris) and other batoid fish. These creatures are highly maneuverable but are also able to cruise at high speeds over long distances. In this paper the structural foundation for the biomimetic morphing wing is a tensegrity structure. A preliminary procedure is presented for developing morphing tensegrity structures that include actuating elements. To do this, the virtual work method has been modified to allow for individual actuation of struts and cables. The actuation response of tensegrity beams and plates are studied and results are presented. Specifically, global deflections resulting from actuation of specific elements have been calculated with or without external loads. Finally, a shape optimization analysis of different tensegrity structures to the biological displacement field will be presented.Dealing with the interaction between numerous bodies, as in granular media, requires larger and larger computational resources. To this end, we develop a domaindecompositionlike method suited to discrete systems with diffuse nonsmoothness. A multiscale enrichment completes the numerical strategy with the extra hope of bridging the gap between discrete and continuum models. The equilibrium of a tensegrity structure, closer to the continuous media case, is chosen to test this approach. (c) 2006 Elsevier Ltd. All rights reserved..In this paper we consider vibration control of tensegrity structures under stationary and nonstationary random excitations. These excitations may be representative of many physical loading conditions, such as earthquake, wind, aerodynamic and acoustic excitations. The optimal control theory based on H2 and Hinfinity controller with full state and limited state feedback is used for the control. The response of the tensegrity structure is represented by the zero lag covariance matrix and the same is obtained by solving the matrix Lyapunov equation. The force generated by the electromechanical coupling of the piezoelectric actuator is used in the formulation. A tensegrity structure of class1 comprising of two modules, with 24 pretension cables and six struts with piezoelectric actuators, is considered.Responsive behavior, which is intrinsic to natural systems, is becoming a key requirement for advanced artificial materials and devices, presenting a substantial scientific and engineering challenge. We designed dynamic actuation systems by integrating highaspectratio silicon nanocolumns, either freestanding or substrateattached, with a hydrogel layer. The nanocolumns were put in motion by the "muscle" of the hydrogel, which swells or contracts depending on the humidity level. This actuation resulted in a fast reversible reorientation of the nanocolumns from tilted to perpendicular to the surface. By further controlling the stress field in the hydrogel, the formation of a variety of elaborate reversibly actuated micropatterns was demonstrated. The mechanics of the actuation process have been assessed. Dynamic control over the movement and orientation of surface nanofeatures at the micron and submicron scales may have exciting applications in actuators, microfluidics, or responsive materials.CStability conditions for tensegrity structures are derived based on positive definiteness of the tangent stiffness matrix, which is the sum of the linear and geometrical stiffness matrices. A necessary stability condition is presented by considering the affine motions that lie in the nullspace of the geometrical stiffness matrix. The condition is demonstrated to be equivalent to that derived from the mathematical rigidity theory so as to resolve the discrepancy between the stability theories in the fields of engineering and mathematics. Furthermore, it is shown that the structure is guaranteed to be stable, if the structure satisfies the necessary stability condition and the geometrical stiffness matrix is positive semidefinite with the minimum rank deficiency for nondegeneracy. (C) 2006 Elsevier Ltd. All rights reserved.MTension members with a zero rest length allow the construction of tensegrity structures that are in equilibrium along a continuous path of configurations, and thus exhibit mechanismlike properties; equivalently, they have zero stiffness. The zerostiffness modes are not internal mechanisms, as they involve firstorder changes in member length, but are a direct result of the use of the special tension members. These modes correspond to an infinitesimal affine transformation of the structure that preserves the length of conventional members, the< y hold over finite displacements and are present if and only if the directional vectors of those members lie on a projective conic. This geometric interpretation provides several interesting observations regarding zero stiffness tensegrity structures. (C) 2007 Elsevier Ltd. All rights reserved.We present a new coordinated control law for a group of vehicles in the plane that stabilizes an arbitrary desired group shape. The control law is derived for an arbitrary shape using models of tensegrity structures which are spatial networks of interconnected struts and cables. The symmetries in the coupled system and the energymomentum method are used to investigate stability of relative equilibria corresponding to steady translations of the prescribed rigid shape.OThis paper focuses on the study of tensegrity active control in situations of partially defined loading and damage events. Selfdiagnosis and selfrepair methodologies are proposed and validated experimentally on a fullscale active tensegrity structure. Selfdiagnosis involves load identification and damage location. The response of the structure to a load and damage is measured and compared with the response of the structure to candidate solutions for load and damage. Selfdiagnosis solutions result in sets of candidate solutions for loads and damage. These solutions are employed to compute control commands of shape control and selfrepair for the structure. Selfrepairing control commands increase stiffness and decrease stresses with respect to the damaged state. Selfrepairing control commands are computed using a multiobjective approach. The application of a control command results in selfstress modifications by changing the length of active struts. The proposed methodologies are attractive for tensegrity active control in situations of partially defined loading and damage events.This paper presents a mechanical analysis of a spatial 1DOF tensegrity mechanism created by connecting three planar tensegrity mechanisms to form a triangular prism. The subsequent investigation produced kinematic and dynamic models that allow the workspaceboundary singularities and minimum energy configuration to be determined. Singularities were found to occur when the mechanism is folded in the vertical X, Y plane or in the horizontal X, Z plane. The minimum energy configuration, formed by the angle between the horizontal plane and the actuated strut, was found to be theta = pi/4. However, when the system was linearized to determine the analytic solution for the dynamics, the minimum energy configuration become 0 = 1 due to the inherent error produced by the system linearization. The dynamic response of the mechanism to an initial small displacement was determined for each case of critically damped, overdamped, and underdamped systems.We give an algorithm for solving the formfinding problem, that is, for finding stable placements of a given tensegrity structure. The method starts with a known stable placement and alters edge lengths in a way that preserves the equilibrium equations. We then characterize the manifold to which classical tensegrity systems belong, which gives insight into the formfinding process. After describing several special cases, we show the results of a successful test of our algorithm on a large system.Aquaculture is the fastest growing food producing sector in the world. Considerable interest exists in developing open ocean aquaculture in response to a shortage of suitable, sheltered inshore locations. The harsh weather conditions experienced offshore lead to a focus on new structure concepts, remote monitoring and a higher degree of automation in order to keep the cost of structures and operations within an economically viable range. This paper proposes tensegrity structures in the design of flexible structures for offshore aquaculture. The finite element analysis program ABAQUS (TM) has been used to investigate stiffness properties and performance of tensegrity structures when subjected to various forced deformations and hydrodynamic load conditions. The suggested concept, the tensegrity beam, shows promising stiffness properties in tension, compression and bending, which are relevant for development of open ocean aquaculture construction for high energy environments. When designing a tensegrity beam, both prestress and spring stiffness should be considered to ensure the desired structural properties. A large strength to mass ratio and promising properties with respect to control of geometry, stiffness and vibration could make tensegrity an enabling technology for future developments.Physical models are constructed to demonstrate Complex Systems Behaviours  MasterSlave Complex, Contract Relationships & Monopolistic Behaviours. These hypotheses are based on the analysis of individual human vertebral neck movements recorded from cinexradiographic stopframe. Pendular beating of the vertebral column was interpreted as a complex system of relationships where segments act as a chain of independent pendulums held in juxtaposed appropinquity. Behavioural phenomenon may also be seen in tensegrity columns and tall yacht masts as a form of dominant/recessive beating. Physical and mathematical models of systems are presented where a threshold is reached, a point of criticality, producing destructive harmonies  a form of emergent behaviour.Tensegrity structures can give a new approach to the construction of mobile robots with different shapes and properties that usual robots, wheeled or legged, do not have. Tensegrity are light, deformable structures that may be able to adapt their form to unconstrained environments. The main issue of this paper is to present the dynamic equations of motion for such structures, analysed from a Lagrangian point of view, and thinking in using them as mobile robots of arbitrary form and size.During numerous biological processes, cell adhesion, cell migration and cell spreading are vital. These basic biological functions are regulated by the interaction of cells with their extracellular environment. To examine the morphology and mechanical changes occurring in mesenchymal stem cells cultured on a mechanically rigid substrate, atomic force microscopy and fluorescence microscopy were employed. Investigations of the cells revealed both linear and geodesic Factin configurations. No particular cell characteristics or intracellular location were implicated in the appearance of the geodesic structures. However, the length of time the cells were cultured on the substrate correlated with the percentage appearance of the geodesic structures. Calculating energy dissipation from cell images acquired by dynamic mode atomic force microscopy, it was observed that the vertices of the geodesic structures had significantly higher energy dissipation compared to the linear Factin and the glass. This supports work by Lazarides [J. Cell Biol. 68, 202219, 1976], who postulated that the vertices of these geodesic structures should have a greater flexibility. Our results also support predictions based on the microfilament tensegrity model. By understanding the basic principles of cell ultrastructure and cell mechanics in relation to different extracellular environments, a better understanding of physiological and pathological process will be elicited.Tensegrities are unique, spacefilling structures consisting of disjoint rigid elements (rods) connected by tensile elements (strings), which hold their shape due to a synergistic balance of opposing forces. Due to their complexity there are few effective analytical methods for discovering new, and particularly, large irregularly shaped tensegrity structures. Recent efforts using evolutionary search have been moderately successful, but have relied upon a direct encoding of the structure, and therefore face scalability issues [3]. By contrast we employ to a developmental representation grammatically "grow" tensegrity structures, and is such, issues of scalability, both in terms of representation and of performance, are addressed. Specifically we evolve map Lsystems [4] which produce planar graphs [1, 2] corresponding to the st< ructural elements of a tensegrity. Each tensegrity is then reproduced within the Open Dynamics Engine (ODE), and the volume of the convex hull described by the final location of the rigid element endpoints used as fitness. As shown in Figure 1, the map Lsystem significantly outperforms the direct encoding across all runs. Figure 2 shows a, representative evolved tensegrity.This study focuses on learning of control commands identification and load identification for active shape control of a tensegrity structure in situations of unknown loading event. Control commands are defined as sequences of contractions and elongations of active struts. Casebased reasoning strategies support learning. Simple retrieval and adaptation functions are proposed. They are derived from experimental results of load identification studies. The proposed algorithm leads to two types of learning: reduction of command identification time and increase of command quality over time. In the event of no retrieved case, load identification is performed. This methodology is based on measuring the response of the structure to current load and inferring the cause. It provides information in order to identify control commands through multiobjective search. Results are validated through experimental testing.This paper presents a fullscale active tensegrity structure at EPFL and demonstrates how it can learn as well as carry out selfdiagnosis and selfcompensation. Tensegrities are generally flexible structures: small loads may lead to large displacements. We thus control slope by actively modifying the selfstress state between cables and struts. The structure benefits from past experience through casebased reasoning. It memorizes past control commands and adapts them in order to react to new applied loads up to forty times more rapidly than without this previous control information. Redundancy of this structure provides opportunities for "fault tolerant" behavior. The active control system can also be used to perform selfdiagnosis and then to selfcompensate local damage. For many cases of local damage, the structure remains capable of satisfying control goals. This paper also summarizes a multiobjective optimization method for control according to four criteria. In contrast with other applications involving multiple objectives, such as design where users prefer choices, this is a control task, thereby requiring identification of a single solution only. Also, the single dominant objective usually generates hundreds of possible solutions. Four objectives are evaluated firstly using Pareto optimality and then a unique solution is chosen through successive filtering of candidate solutions using a hierarchy of objectives. The combination of advanced computing techniques with structural control of serviceability criteria is providing many new possibilities for structural engineers. These results are expected lead toward more autonomous and selfadaptive structures that are able to evolve as their environment changes.aOne of the drawbacks of conventional mechanisms is the significant inertia of their moving parts. Tensegrity mechanisms, which have a reduced mass because of their extensive use of cables and springs, represent a potential alternative to these mechanisms for certain types of applications. In this paper a new spatial threedegreeoffreedom tensegrity mechanism is developed and analyzed. Mathematical models of the kinematics, statics, and dynamics of the mechanism are generated. These models reveal several characteristics of the fundamental behavior of tensegrity mechanisms that make them rather unique.Tensegrity mechanisms are lightweight, deployable and can be accurately modeled. Consequently, they constitute an interesting alternative to conventional mechanisms for some applications. In this work, the kinematics, statics and dynamics of a planar twodegreeoffreedom tensegrity mechanism are studied. Solutions to the direct and inverse static problems are first presented. Afterwards, the boundaries of the actuator and Cartesian workspaces of the mechanism are computed. The stiffness of the mechanism is then detailed for different situations. Finally, a dynamic model is derived and a preliminary control scheme is proposed. (C) 2005 Elsevier Ltd. All rights reserved.gThe ability to model the mechanical behaviour of the cell cytoskeleton as realistically as possible is a key point in understanding numerous biological mechanisms. Tensegrity systems have already demonstrated their pertinence for this purpose. However, the structures considered until now are based only on models with simplified geometry and topology compared to the true complexity of cytoskeleton architecture. The aim of this Note is to propose a formfinding method for generating nonregular tensegrity shapes of higher diversity and complexity. The process relies on the use of the dynamic relaxation method. Further improvements have made it possible to control the computed morphologies and to modify them to approach experimentally observed configurations. Various examples illustrate the use of the method and the results obtained for different cell typologies.This is an overview of some of the similarities and differences between structures such as frameworks and cabled tensegrities in the hyperbolic plane and hyperbolic space on the one hand and the Euclidean plane, the sphere and Euclidean space on the other hand.A formfinding problem for tensegrity structures is studied; given an abstract graph, we show an algorithm to provide a necessary condition for it to be the underlying graph of a tensegrity in Rd (typically d = 2,3) with vertices in general position. Furthermore, for a certain class of graphs our algorithm allows to obtain necessary and sufficient conditions on the relative position of the vertices in order to underlie a tensegrity, for what we propose both a geometric and a symbolic approach.RThis paper proposes and demonstrates a symbolic procedure to compute the stiffness of truss structures built up from simple basic units. Geometrical design parameters enter in this computation. A set of equations linear in the degreesoffreedom, but nonlinear in the design parameters, is solved symbolically in its entirety. The resulting expressions reveal the values of the design parameters which yield desirable properties for the stiffness or stiffnesstomass ratio. By enumerating a set of topologies, including the number of basic units, and a set of material distribution models, stiffness properties are optimized over these sets. This procedure is applied to a planar tensegrity truss. The results make it possible to optimize the structure with respect to stiffness properties, not only by appropriately selecting (continuous) design parameters like geometric dimensions, but also by selecting an appropriate topology for the structure, e.g., the number of basic units, and a material distribution model, all of which are discrete design decisions. (c) 2005 Elsevier Ltd. All rights reserved.This paper proposes and demonstrates procedures to optimally design tensegrity structures actuation, based on closed loop shape control requirements, while at the same time a feasible path for realizing a desired shape is synthesized. The procedures are employing different optimization based formulations of a set of requirements needed for shape control. The specific procedure demonstrated is based on a mixed integer linear programming formulation, one of the simplest possible. It is possible to formulate the design problem more generally, but then the computations become more involved, inhibiting a real time implementation of the procedure. The demonstration is for a simple planar tensegrity, but the procedures can be applied to more general structures without modification.)Sophisticated loadcarrying structures, in nature as well as manmade, share some common properties. A clear differentiation of tension, compression and shear is in nature primarily manifested in the properties of materials adapted to the efforts, whereas they in engineering are distributed on different components. For stability and failure saf< ety, redundancy on different levels is also commonly used. The paper aims at collecting and expanding previous methods for the computational treatment of redundant and forcedifferentiated systems. A common notation is sought, giving and developing criteria for describing the diverse problems from a common structural mechanical viewpoint. From this, new criteria for the existence of solutions, and a method for treatment of targeted dynamic solutions are developed. Added aspects to previously described examples aim at emphasizing similarities and differences between engineering and nature, in the forms of a tension truss structure and the human musculoskeletal system. (c) 2005 Elsevier B.V. All rights reserved.]A novel and versatile numerical formfinding procedure that requires only a minimal knowledge of the structure is presented. The procedure only needs the type of each member, i.e. either compression or tension, and the connectivity of the nodes to be known. Both equilibrium geometry and force densities are iteratively calculated. A condition of a maximal rank of the force density matrix and minimal member length, were included in the formfinding procedure to guide the search of a state of selfstress with minimal elastic potential energy. It is indeed able to calculate novel configurations, with no assumptions on cable lengths or cabletostrut ratios. Moreover, the proposed approach compares favourably with all the leading techniques in the field. This is clearly exemplified through a series of examples. (c) 2006 Elsevier Ltd. All rights reserved.In this paper, a nonlinear structural analysis software with proprocessing and postrecessing function is proposed by the author. The software incorporating the functions of the structural analysis and geometrical design of Tensegrity structures. Using this software, Cable Dome is analyzed as a prototype, a comprehensive study on the structural behavior of Tensegrity domes is presented in detail. Design methods of Tensegrity domes were proposed. Based on the analysis, optimizing design was performed. Several new Tensegrity domes with different geometrical design scheme are proposed, the structural analysis of the new schemes is also conducted. The analysis result shows that the proposed new forms of the Tensegrity domes are reasonable for practical applications.We define a tensegrity factor, t(00)(+/), for XMX linkages of gasphase MXn compounds (X is an atom of an insulating element) that is a measure of the matching of 'ideal' 1,2(singlebonded) MX distance, d(MX)(00), to the 'ideal' (nonbonded) 1,3XX distances, d(MX)(00). The actually observed 1,3distance, d(XX) is given (within 1% error) by 2CR(X)/FS, where FS (= 21.41(00)(+/)) is shown to be an ab initio quantity with no adjustable parameter, no dependence on actual MX distance or bond order and with 2CR(X) depending only on whether M is an atom of an insulating element (2CR(X) =d(XX)(00)) or whether M is metallic (2CR(X) = 1.1d(XX)(00)). This is illustrated for gasphase MX2 compounds.This article extends an earlier definition(1) and use of molecular tensegrity for obtaining quantitatively the 1,3nonbonded distances in gasphase MX2 compounds to nearly 160 gasphase MXn (n <= 4) inorganic compounds (including those of transition metal elements), once a transferable 'core' atomic size is specified. The simple principles behind this methodology (involving only linear equations), its quantitative character, its transparency, its portability and its generality account very simply for molecular geometry in such compounds without requiring earlier theoretical methodologies. We also establish clear distinction in the prescription for obtaining the 1,3distance when M is an atom of a metallic or insulating element.$A simple derivation of the tangent stiffness matrix for a prestressed pinjointed structure is given, and is used to compare the diverse formulations that can be found in the literature for finding the structural response of prestressed structures. (c) 2005 Elsevier Ltd. All rights reserved.pDevelopmental biology describes how tissues, organs, and bodies are made from living cells. There exists a large body of biological data about developmental processes but there is still not ultimate understanding of how the whole orchestra of all involved processes is working. It is the place where mathematical modelling could help to create biologically relevant models of morphological development. The morphological development could be mathematically decomposed into three distinct but mutually interconnected parts, namely to mechanical response of tissues, signalling by chemicals, and switching of cells into different types by a gene regulatory network. This paper is focussed to the part dealing with mechanical interaction of growing mesenchyme and epithelium within a living tissue modelled by a set of nodes interconnected by deformable bars as in tensegrity models.Stability studies of a tensegrity structure, used as a model for cell deformability, are performed. This structure is composed by six slender struts interconnected by 24 linearly elastic tendons and is prestressed. The tendons and the struts are governed by linear constitutive laws. The struts are allowed to buckle. Since the deformations are large, mathematical bifurcation theory working mainly for small deformations does not work. A general procedure for studying the stability behavior of the particular tensegrity model based upon the elastica theory is presented. The reference placement is defined by the prestress and the equilibrium placements are defined for any applied threedimensional forces.Stability studies of a tensegrity structure, used as a model for cell deformability, are performed. This structure is composed of 6 slender struts interconnected by 24 linearly elastic cables. The cables and the struts are governed by linear constitutive laws. The struts are allowed to buckle. Adapting experimental evidence, the struts have already buckled at the reference placement due to the prestress of the tendons. A general procedure for studying the stability behavior of the particular tensegrity model is presented. The reference placement is defined by the prestress, and the equilibrium placements are defined for any threedimensional applied forces.This paper concerns prestress optimization of a tensegrity structure for its optimal LQR performance. A linearized dynamic model of the structure is derived in which the forcedensity variables that parameterize the prestress of the structure appear linearly. A feasible region for these parameters is defined in terms of the extreme directions of the prestress cone. A numerical method for computing this basis for a structure prestress cone is proposed. The problem is solved using a gradient method that provides a monotonic decrease of the objective function inside the feasible region. A numerical example of a cantilevered planar tensegrity beam is shown. (c) 2005 Elsevier Ltd. All rights reserved.This paper concerns the design of tensegrity structures with optimal masstostiffness ratio. Starting from an initial layout that defines the largest set of allowed element connections, the procedure seeks the topology, geometry and prestress of the structure that yields optimal designs for different loading scenarios. The design constraints include strength constraints for all elements of the structure, buckling constraints for bars, and shape constraints. The problem formulation accommodates different symmetry constraints for structure parameters and shape. The static response of the structure is computed by using the nonlinear large displacement model. The problem is cast in the form of a nonlinear program. Examples show layouts of 2D and 3D asymmetric and symmetric structures. The influence of the material parameters on the optimal shape of the structure is investigated. (c) 2005 Elsevier Ltd. All rights reserved.The static properties of tensegrity structures have been widely appreciated in civil engineering as the basis of extremely lightweight yet strong mechanical structures. However, the dynamic properties and t< heir potential utility in. the design of robots have been relatively unexplored. This paper introduces robots based on tensegrity structures, which demonstrate that the dynamics of such structures can be utilized for locomotion. Two tensegrity robots are presented: TR3, based on a triangular tensegrity prism with three struts, and TR4, based on a quadrilateral tensegrity prism with four struts. For each of these robots, simulation models are designed, and automatic design of controllers for forward locomotion are performed in simulation using evolutionary algorithms. The evolved controllers are shown to be able to produce static and dynamic gaits in both robots. A realworld tensegrity robot is then developed based on one of the simulation models as a proof of concept. The results demonstrate that tensegrity structures can provide the basis for lightweight, strong, and faulttolerant robots with a potential for a variety of locomotor gaits.Stability studies of a T3 tensegrity structure are performed. This structure is composed of three slender struts interconnected by six nonlinear elastic tendons and is prestressed. The struts are governed by linear constitutive laws and are allowed to buckle. Since tensegrity is used for modeling structures with quite large deformations, for example the cytoskeleton, and bifurcation theoryvalid for small solutions of the nonlinear equationsdoes not directly apply, a general procedure for studying the stability behavior of the particular tensegrity model based upon the elastica theory is presented. The reference placement is defined by the prestress, and the equilibrium placements are defined by the applied force and moment. The potential applications of tensegrity structures are not only increasing in civil engineering but also in fields like biomechanics. The key step in designing tensegrity, the formfinding problem, has been investigated by many researchers but until now they have tended to focus on methods for regular shapes. Since there is an increasing need for design tools devoted to more various and complex systems, the objective of this paper is to present the formfinding of nonregular tensegrity structures with a numerical approach. It is based on the dynamic relaxation method with kinetic damping, and new tensegrity configurations in more intricate and creative forms can be obtained this way. During the formfinding process, either the force or length of some elements can be fixed by an appropriate choice of related stiffnesses. The application of the process is illustrated by several numerical examples. It can be concluded that an improvement in tensegrity formfinding has been achieved extending research from regular shapes toward "freer" shapes.{in the process of designing a tensegrity system, some constraints are usually introduced for geometry and/or forces to ensure uniqueness of the solution, because the tensegrity systems are underdetermined in most cases. In this paper, a new approach is presented to enable designers to specify independent sets of axial forces and nodal coordinates consecutively, under the equilibrium conditions and the given constraints, to satisfy the distinctly different requirements of architects and structural engineers. The proposed method can be used very efficiently for practical applications because only linear algebraic equations are to be solved, and no equation of kinematics or material property is needed. Some numerical examples are given to show not only efficiency of the proposed method but also its ability of searching new configurations. (c) 2005 Elsevier Ltd. All rights reserved.A numerical method is presented for formfinding of tensegrity structures. Eigenvalue analysis and spectral decomposition are carried out iteratively to find the feasible set of force densities that satisfies the requirement on rank deficiency of the equilibrium matrix with respect to the nodal coordinates. The equilibrium matrix is shown to correspond to the geometrical stiffness matrix in the conventional finite element formulation. A unique and nondegenerate configuration of the structure can then be obtained by specifying an independent set of nodal coordinates. A simple explanation is given for the required rank deficiency of the equilibrium matrix that leads to a nondegenerate structure. Several numerical examples are presented to illustrate the robustness as well as the strong ability of searching new configurations of the proposed method. (c) 2005 Published by Elsevier Ltd.NOVELTY  The struts are tied together at several internal strut nodal minimum of the desired resonate mode for strut, so that several struts become the resonating elements. USE  For converting tensegrity structures into musical instruments such as wind chimes. ADVANTAGE  Facilitates overtone dampening and increased structural integrity. DETAILED DESCRIPTION  INDEPENDENT CLAIMS are also included for the following: (1) multimode resonating chimes; (2) single or multimodal chime; and (3) method of exploiting inherent ability of tensegrities struts to share applied stress with struts adjacent to it to accomplish desired cross coupling of resonators in multiresonator tensegrity.In this paper, we propose a form finding analysis method for Tensegrity structures based on the variational method. Tensegrity structures are spatial structures formed by a combination of struts and ties [I]. No pair of struts touches and ties connect the end of each strut. The struts are always in compression and the ties in tension. The entire configuration is in selfequilibrium state and the final form of Tensegrity structures is determined so as to satisfy this equilibrium state. In this paper, struts and ties are modeled by rigid elements and elastic cable elements respectively. The variational formulation is firstly derived to minimize the total potential energy of cable elements with the constraint conditions for keeping the length of rigid elements constant and then the discretized nonlinear equations are solved by using the NewtonRaphson method [2]. Finally, several novel examples of Tensegrity structures that have Diamond, Zigzag and optional forms are demonstrated to validate the proposed method.In this paper, we present a multiobjective optimization approach for force design of tensegrity structures, where their geometries are assumed to be determined a priori; we search for the optimal distribution of member forces that leads to the maximum stifftiess, and that is closest to the target values assigned by the designers as well. The Pareto optimal solutions of the problem are presented for a tensegrity grid as an example to demonstrate the methodology.Tensegrity mechanisms have the advantage of being relatively lightweight due to their extensive use of cables and springs. In this work, a novel planar modular 2DoF tensegrity mechanism that is actuated by cables is introduced. The modular architecture of the mechanism gives it increased flexibility while using cables for the actuation leads to large reachable workspaces. An analysis of the mechanism's statics and kinematics is performed for the case where no external loads are acting.Certain kinds of mollusks can perform flexible actions by changing body shape. Octopi, in particular, have little in the way of a skeletal structure, and their body frame consists mostly of muscular fibers roughly equivalent to actuators. Here, we have applied tensegrity structure[3,1,2] as a flexible body structure, just as the muscular fibers of an octopus. This tensegrity structure is used in a robot that moves by changing form, creating various shapes in the process. Since the most effective means of movement in the case of a simple body is rotation, sensor information fluctuates drastically. Here, we assess control of such a robot by rulebased general reinforcement learning and by a recurrent neural network using neural oscillators. When reinforcement learning was used, because the sensor information is prone to drastic change, the robot had only a small number of chances to learn in each state, making effective control regardless of the state difficult. However, a certain lev< el of control was possible during conditions in which the sensor information did not alter as significantly. When neural oscillators were used, a considerable amount of time was required for updating link weights, but smooth movement was achieved because of the rhythm generated by the oscillators.Tensegrity robots with backlash free motion control functionality are considered. Without introducing any linktolink motors, the proposed system achieves controllability by a motorizedpulley tendon actuation network. Due to the mechanical coupling between two motorizedtendons and two robotic manipulators, the proposed actuation system maintains a surjective mapping from the space of admissible tendon forces to the space of singularity free maneuvers of the individual serialchain manipulators (provided the links remain noncontacting). For this new class of snakelike robots, a position feedback motion control law is developed that minimizes the maximum motor torque while ensuring that the tendons do not go slack at any point along a given robot trajectory. Numerical simulations illustrate the method and demonstrate tensegrity's superior maneuvering and backlash avoidance capabilities.In this paper the sensor/actuator selection for the control of tensegrity structures is investigated from a system design approach. Two methods with different levels of complexity are proposed to find the necessary precision for each sensor/actuator to satisfy specific input/output performance constraints. To determine the minimum number and the locations of the sensors and actuators, a heuristic algorithm iteratively deletes the sensor or actuator which requires the least precision until loss of feasibility. This algorithm results simultaneously the necessary number, the location and precision for each sensor/actuator. A tensegrity structure example has been solved as an application of the proposed algorithms.The paper traces down the roots of the first manmade objects which resemble what are nowadays known as tensegrity structures and then shows how the tensegrity concept evolved, finding increasingly large audiences in engineering, mathematics, and biology.Current attempts to build fast, efficient, and maneuverable underwater vehicles have looked to nature for inspiration. However, they have all been based on traditional propulsive techniques, i.e. rotary motors. In the current study a promising and potentially revolutionary approach is taken that overcomes the limitations of these traditional methods  morphing structure concepts with integrated actuation and sensing. Inspiration for this work comes from the manta ray (Manta birostris) and other batoid fish. These creatures are highly maneuverable but are also able to cruise at high speeds over long distances. In this paper, the structural foundation for the bioinspired morphing wing is a tensegrity structure. A preliminary procedure is presented for developing morphing tensegrity structures that include actuating elements. A shape optimization method is used that determines actuator placement and actuation amount necessary to achieve the measured biological displacement field of a ray. Lastly, an experimental manta ray wing is presented that measures the static and dynamic pressure field acting on the ray's wings during a normal flapping cycle.Tensegrity structures are an emerging paradigm that facilitates the integration of structures and control technologies. We expect tensegrity to play a major role in future controlled structures and materials. In this paper we address the problem of designing tensegrity structures which possess minimal mass. We show that this problem can be solved analytically for regular and symmetric tensegrity towers and plates in a way that is essentially independent of the material properties. This is typical result in tensegrity systems, where the properties of the structure are greatly dictated by its geometry, hence being scalable, rather then by the choice of materials.Tensegrity structures are a class of mechanical structures which are highly controllable. These smart structures have a large number of potential applications, for the benefit of systems which need, for instance, a small transportation or storage volume, tunable stiffness properties, active vibration damping and deployment or configuration control. We model tensegrity structures as mechanical trusses made of bars and strings. The bars, assumed to be rigid rods, are held in stable equilibrium by a continuous network of strings in tension. The dynamic equations of motion for rigid rods are differentialalgebraic equations of motion, derived on a nonminimal coordinate system with an associated dynamic algebraic constraint. The use of differentialalgebraic equations of motion simplifies the system description but introduce some challenges for control design. This paper introduces and compares two different Lyapunov based control design methodologies for tensegrity structures. The theory is developed and illustrated on the simplest possible example of a threedimensional controlled tensegrity system, a pinned bar actuated by three strings.This paper investigates the potential of controlled tensegrity structures as a means for electrically generating and storing energy injected into the structure by external disturbances. An approach is presented for the integration of linear, regenerative actuators into tensegrity structures as supplemental active bars. By operating these actuators as generators, mechanical energy absorbed from the structure during periods of external excitation is converted to electrical energy. Through proper control of the powerelectronic network to which the actuators are connected, a fraction of this energy may be recovered and delivered to a storage system or an external power grid. A generalized model for a regenerative tensegrity structure with arbitrarilymany actuators is presented, which accounts for electrical dissipation in the actuators and associated electronics. Issues pertaining to actuator selection and powerelectronic control are discussed. An approach is presented for the design of simple collocated linear velocityfeedback controllers for systems with one actuator, such that the rate of structural energy extraction is optimized for the steadystate closedloop response to an external disturbance. The approach is illustrated in a simulation example for a smallscale system. Extensions are discussed in which a regenerative tensegrity structure is used to harvest energy from the motion of ocean waves.>In this paper we discuss the derivation and numerical implementation of the equations of motion for mechanical systems with rods. These equations of motion find application in the analysis and simulation of Class 1 Tensegrity Structures. In the first part of the paper we present detailed derivations of two distinct sets of differential equations, both using nonminimal sets of coordinates. In the second part of the paper we present the result of some numerical experiments, comparing the performance of these equations in the context of numerical integration algorithms.Rather than the traditional vector differential equation, this paper introduces rigid body dynamics in a new form, as a matrix differential equation. We focus on axisymmetric rigid bodies which are adequate to describe a large class of problems, including tensegrity systems. For a system of,3 rigid bodies, the forces are characterized in terms of network theory, and the kinematics are characterized in terms of the bar vectors (directed connections between two nodes attached to a rigid body). The dynamics are characterized by a second order differential equation in a 3 x 20 configuration matrix. The first contribution of the paper is the dynamic model of a broad class of systems of rigid bodies, characterized in a compact form, requiring no inversion of a variable mass matrix. The second contribution is the derivation of all equilibria as a linear algebra problem in the control variables. The third contribution is the derivation of a linear model of the system of rigid bodies. One significance of these equations is the ex< act characterization of the statics and. dynamics of all class 1 tensegrity structures, where rigid bar lengths are constant and the string force densities are control variables, which appear linearly. This will offer a significant advantage in control design tasks.fSandwich panels with truss cores offer possibilities for selfactuation. They are analyzed, with emphasis on mass optimal design for failure and stiffness. It is shown that introducing additional freedom in selecting the topology of tetrahedral or pyramidal cores, by 1) making the core units, or even all core members, disjoint, so varying the distance between core units becomes possible, 2) using multiple layers, brings significant advantages. For some conditions, the performance of the modified panel becomes better by a factor of two, causing actuated truss core panels to perform at least as well as, or even better than, panels with, e.g., honeycomb cores, that do not easily allow core actuation. A special case of the analysis is the mass optimal design of panels with 3DKagome truss units, which can be regarded as a special geometry for a tensegrity prism.Recently, Connelly and Sloughter [14] have introduced the notion of drealizability of graphs and have, among other things, given a complete characterization of the class of 3realizable graphs. However, their work has left open the question of finding an algorithm for realizing those graphs. In this paper, we resolve that question by showing that the semidefinite programming (SDP) approach of [11, 32] can be used for realizing 3realizable graphs. Specifically, we use SDP duality theory to show that given a graph G and a set of lengths on its edges, the optimal dual multipliers of a certain SDP give rise to a proper equilibrium stress for some realization of G. Using this result and the techniques in [14, 31], we then obtain a polynomial time algorithm for (approximately) realizing 3realizable graphs. Our results also establish a littleexplored connection between SDP and tensegrity theories and allow us to derive some interesting properties of tensegrity frameworks.$For a general class of HyperActuated MechanicalSystems (HAMS) that is generalized to include robotic manipulators and tendondriven tensegrity structures, this paper determines the tendon force inputs from a set of admissible, nonsaturating inputs, that will move the rigidbody system from point A to point B along a prescribed path with minimum time and control energy. The approach herein utilizes the existence conditions and solution of a linear algebra problem that describes how the set of admissible tendon forces is mapped onto the set of pathdependent torques. Since this mapping is not onetoone, free parameters in the control law always exist. This paper determines the best timeinvariant free parameters. This yields a novel control law for HAMS that tracks the center of the admissible set and reduces the number of states in the optimal control problem. to two. The prevalence of HAMS in nature is discussed. Numerical examples illustrate the method and demonstrate tensegrity's superior maneuvering and saturation avoidance capabilities.Tensegrity mechanisms have the advantage of being relatively lightweight due to. their extensive use of cables and springs. As such, they have the potential of being an attractive alternative to conventional mechanisms in certain application environments. However, the presence of unconstrained degrees of freedom in tensegrity mechanisms leads to a dynamic behaviour that cannot be directly controlled with the actuators. In this work, the dynamic model of a novel spatial threedegreeoffreedom (3DOF) tensegrity mechanism is developed using the Lagrangian formulation. The resulting equations of motion are then solved to simulate the mechanism's motion between equilibrium configurations. Since the mechanism is subjected to holonomic nonlinear geometrical constraints, these must be considered during the solution of its forward dynamic problem. It is seen that the use of damping in the springs is not very efficient in dissipating the mechanism's energy during motion.<The use of tensegrity systems as structures has been extensively studied. However their development for use as mechanisms is quite recent even though they present such advantages as reduced mass and a deployment capability. The object of this paper is to apply analysis methods usually reserved for conventional mechanisms to a planar onedegreeoffreedom tensegrity mechanism. This mechanism is obtained from a threedegreeoffreedom tensegrity system by adding actuation to the latter as well as by making some assumptions of symmetry. Analytical solutions are thus developed for the mechanism's direct and inverse static problems. Furthermore, the working curve, singularities, and stiffness of the mechanism are detailed. Finally, a dynamic model of the mechanism is developed and a preliminary control scheme is proposed.Tensegrity systems are selfstressed reticulate space structures. As lightweight frames, they are subject to deformation and vibration issues when faced to natural stimulations such as temperature gradients or wind. Classical passive solutions impose to rigidify components or to add damping in the structure using heavy devices. Active systems, mainly developed in space and seismic fields, are controlled using external energy brought by activators. We describe in this paper a mixed geometric and dynamic active control of tensegrity structures using a robust control design technique. An experiment is carried out on a six selfstress states plane tensegrity grid.Here some ideas related with delayed unstable systems are exposed. In particular, two simple dynamics where antagonistic forces, one of them being a timedelayed and randomly modulated force, are presented as prototypes to study the apparency of a critical balance that is seen as a transient stabilization of the system. This type of dynamics allows for the control of the unstable state overcoming limitations imposed by time latencies. (c) 2005 Elsevier B.V. All rights reserved.}Two problems are addressed in this paper. First, the mathematical model to perform the static analysis of an antiprism tensegrity structure subjected to a wide variety of external loads is presented. The virtual work approach is used to deduce the equilibrium equations and a method based on Newton's Third Law is used to verify the numerical results. Two numerical examples arc provided to demonstrate the use of the mathematical model, as well as the verification method. The second problem deals with the development of a mathematical model to perform the static analysis of a prestressed antiprism tensegrity structure subjected to an arbitrary length reduction of its connecting ties. Again, a virtual work approach is used to deduce the equilibrium equations and the numerical results are verified using a Newtonian approach. One example is provided to illustrate the mathematical model.The inputoutput selection approach followed in this brief uses a rigorous and systematic procedure, efficiently selecting actuators and/or sensors that guarantee a desired level of performance, embedded in a heuristic. The procedure generates all socalled minimal dependent sets and uses a closedloop criterion. The heuristic is a divideandconquer one. This approach is applied to controlled tensegrity structures, using as criterion efficiently computable conditions for the existence of a stabilizing Hinfinity controller achieving a desired level of performance. Structural systems, like controlled tensegrities, are a prime example for application of techniques that address system design issues, because they present opportunities in choosing actuators/sensors and in choosing their mechanical structure. Results for a threeunit planar tensegrity structure, where all 26 tendons can be used as actuator or sensor devices, making up 52 devices from which to choose, demonstrate the approach. Two design specifications were explored, one is related to the dynamical stiffness of the structure, the other to vibration isolation. The feasible sets of actuators an< d sensors depend on the specifications and really differ for both, but are mostly composed of much less than 52 devices.This work investigates the design of a new class of three dimensional tensegrity tower structures with nodes lying on a cylinder. The novel aspect of the proposed topology is the fact that all bars in all stages are oriented in the same way, clockwise or counterclockwise. We investigate the existence of conditions for static equilibrium of such towers with an arbitrary number of stages and uniform force distribution.gTensegrity structures are composed of cables and struts that become stable through self stress. They are good candidates for implementation of active structural control because their flexibility may mean that they cannot meet serviceability criteria. Changes to the self stress influence the form of the structure. A reliable closedform solution for obtaining control commands for telescopic compression elements in order to obtain a required shape does not exist for such a closely coupled and geometrically nonlinear structure. Simulating the structural behavior after all possible control commands and testing against constraints and the objective function requires computational times that grow exponentially with the number of actuators. This paper demonstrates that search time can be reduced through use of stochastic search methods and that incrementally storing successfully applied control commands in a casebased reasoning system increases performance during service lives (learning). Such results demonstrate that enhancing control with advanced computing methods provides opportunities for innovative structures.A comprehensive study on the structural behavior and structural types of Tensegrity domes is presented. The numerical analysis method of Tensegrity structure is also discussed. The first Tensegrity domeGeorgia Dome is analyzed as a prototype through a nonlinear software using the numerical method presented in the paper. Based on the analysis, the structural behavior of the Tensegrity dome is summarized and therefore, some design methods for the Tensegrity dome are proposed. Based on the above studies, several new types of Tensegrity domes with different geometric grids are proposed by the author. A comparison of the structural behavior between the Georgia Dome and the domes proposed by the author is also made. (C) 2004 Elsevier Ltd. All rights reserved.A T3 tensegrity structure composed by three struts and six elastic cables is considered. Adopting delay convention, stability of this model is studied. Two kinds of simple instabilities are investigated. The first is concerned with the global (overall) instability of the model and the second with the localEulerbuckling of the struts. Compound instabilities are also studied. Critical conditions are found and postcritical behavior is described.`An elastic cytoskeletal tensegrity structure composed by six inextensible elastic struts and 24 elastic cables is considered. The model is studied, adopting delay convention for stability. Critical conditions for simple and compound instabilities are defined. Postcritical behavior is also described. Equilibrium states with buckling of the struts are also considered. It is revealed that critical Euler buckling load of the struts is a necessary but not a sufficient condition for the existence of bifurcated equilibrium states, caused by buckling of the struts. (C) 2004 Elsevier Ltd. All rights reserved.pResearchers have constructed a number of DNAbased nanodevices that undergo stepped configuration changes through the application of singlestranded DNA oligomers. Such devices can be incorporated into gel networks to create new classes of active materials with controllable bulk mechanical properties. This concept was demonstrated in a DNAcrosslinked gel, the stiffness of which was modulated through the application of DNA strands. Each crosslink incorporated a singlestranded region to which a DNA strand with a complementary base sequence (called the fuel strand) bound, thereby changing the nanostructure of the gel network. The gel was restored to its initial stiffness through the application of the complement of the fuel strand, which cleared the fuel strand from the crosslink via competitive binding. Stiffness changes in excess of a factor of three were observed. The ability to switch the mechanical properties of these gels without changing temperature, buffer composition, or other environmental conditions, apart from the application of DNA, makes these materials attractive candidates for biotechnology applications.This paper presents a new class of compliant surfaces, dubbed tensegrity fabrics, for the problem of reducing the drag induced by nearwall turbulent flows. The substructure upon which this compliant surface is built is based on the "tensegrity" structural paradigm, and is formed as a stable pretensioned network of compressive members ("bars") interconnected by tensile members ("tendons"). Compared with existing compliant surface studies, most of which are based on springsupported plates or membranes, tensegrity fabrics appear to be better configured to respond to the shear stress fluctuations (in addition to the pressure fluctuations) generated by nearwall turbulence. As a result, once the several parameters affecting the compliance characteristics of the structure are tuned appropriately, the tensegrity fabric might exhibit an improved capacity for dampening the fluctuations of nearwall turbulence, thereby reducing drag. This paper improves our previous work (SPIE Paper 504957) and uses a 3D timedependent coordinate transformation in. the flow simulations to account for the motion of the channel walls, and the Cartesian components of the velocity are used as the flow variables. For the spatial discretization, a dealiased pseudospectral scheme is used in the homogeneous directions and a secondorder finite difference scheme is used in the wallnormal direction. The code is first validated with several benchmark results that are available in the published literature for flows past both stationary and nonstationary walls. Direct numerical simulations of turbulent flows at Retau = 150 over the compliant tensegrity fabric are then presented. It is found that, when the stiffness, mass, damping, and orientation of the members of the the unit cell defining the tensegrity fabric are selected appropriately, the nearwall statistics of the turbulence are altered significantly. The flow/structure interface is found to form streamwisetravelling waves reminiscent of those found at airwater interfaces, but traveling at a faster phase velocity. Under certain conditions, the coupled flow/structure system is found to resonate, exhibiting a synchronized, almost sinusoidal interfacial motion with relatively long streamwise correlation.This paper concerns optimization of prestress of a tensegrity structure to achieve the optimal mixed dynamic and control performance. A linearized dynamic model of the structure is derived. The force density variables that parameterize prestress of the structure appear linearly in the model. The feasible region of these parameters is defined in terms of the extreme directions of the prestress cone. Several properties of the problem are established inside the feasible region of the parameters. The problem is solved using a gradient method that provides a monotonic decrease of the objective function inside the feasible region. A numerical example of a cantilevered planar tensegrity beam is shown.dWe characterize the planned path for a shape change in a tensegrity structure as a path from one equilibrium to another. For tensegrity structures, this means that in every desired configuration the structure has to satisfy tensegrity conditions. Required trajectories are feasible, and changes in potential energy are not required to follow these trajectories. This is a benefit over normal control paths that require strainenergy changes because such energy must be supplied by the control system. For the class of modular tensegrity structures defined, configurations that satisfy tensegrity condit< ions can be parameterized in terms of only a few parameters that can meaningfully be related to the overall desired shape of the structures. Equilibrium rest lengths of string elements are defined first. An openloop restlength control is defined by slowly varying desired geometric parameters, which causes the structure to track trajectories defined by the timedependent geometric parameters. Examples with simulation results show different reconfiguration scenarios of tensegrity plates and class2 tensegrity towers.This paper concerns the formfinding problem for general and symmetric tensegrity structures with shape constraints. A number of different geometries are treated and several fundamental properties of tensegrity structures are identified that simplify the formfinding problem. The concept of a tensegrity invariance (similarity) transformation is defined and it is shown that tensegrity equilibrium is preserved under affine node position transformations. This result provides the basis for a new tensegrity formfinding tool. The generality of the problem formulation makes it suitable for the automated generation of the equations and their derivatives. Stateoftheart numerical algorithms are applied to solve several example problems. Examples are given for tensegrity plates, shellclass symmetric tensegrity structures and structures generated by applying similarity transformation. (c) 2005 Elsevier Ltd. All rights reserved.}This paper demonstrates a method for prestress optimization of tensegrity structures resulting in their optimal mixed dynamic and control performance. Prestress of a structure is parameterized using forcedensity variables that appear linearly in its linearized dynamic model. A feasible region for these parameters is defined in terms of the extreme directions of the prestress cone. A numerical method is proposed for computing this particular basis for the structure prestress cone. The problem is solved using a gradient method based on the sensitivity analysis. A numerical example of a cantilevered planar tensegrity beam is shown.Tensegrity structures have become of engineering interest in recent years, but very few have found practical use. This lack of integration is attributed to the lack of a well formulated design procedure. In this paper, a preliminary procedure is presented for developing morphing tensegrity structures that include actuating elements. To do this, the virtual work method has been modified to allow for individual actuation of struts and cables. A generalized connectivity matrix for a cantilever beam constructed from either a single 4strut cell or multiple 4strut cells has been developed. Global deflections resulting from actuation of specific elements have been calculated. Furthermore, the force density method is expanded to include a necessary upper bound condition such that a physically feasible structure can be designed. Finally, the importance of relative force density values on the overall shape of a structure comprising of multiple unit cells is discussed.The design of legged robots for movement has usually been based on a series of rigid links connected by actuated or passively compliant joints. However, the potential utility of tensegrity, in which form can be achieved using a disconnected set of rigid elements connected by a continuous network of tensile elements, has not been considered in the design of legged robots. This paper introduces the idea of a legged robot(1) based on a tensegrity structure, and demonstrates that the dynamics of such structures can be utilized for locomotion. A mobile robot based on a triangular tensegrity prism is presented, which is actuate by contraction of its transverse cables. The automatic design of a controller architecture for forward locomotion is performed in simulation using a genetic algorithm which demonstrates that the structure can generate multiple effective gait patterns for forward locomotion. A real world tensegrity robot is implemented based on the simulated robot, which is shown to be capable of producing forward locomotion. The results suggest that a tensegrity structure can provide the basis for extremely lightweight and robust mobile robots.The cytoskeleton is not an equilibrium structure. To develop theoretical tools to investigate such nonequilibrium assemblies, we study a statistical physical model of motorized spherical particles. Though simple, it captures some of the key nonequilibrium features of the cytoskeletal networks. Variational solutions of the manybody master equation for a set of motorized particles accounts for their thermally induced Brownian motion as well as for the motorized kicking of the structural elements. These approximations yield stability limits for crystalline phases and for frozen amorphous structures. The methods allow one to compute the effects of nonequilibrium behavior and adhesion (effective crosslinking) on the mechanical stability of localized phases as a function of density, adhesion strength, and temperature. We find that nonequilibrium noise does not necessarily destabilize mechanically organized structures. The nonequilibrium forces strongly modulate the phase behavior and have comparable effect as the adhesion due to crosslinking. Modeling transitions such as these allows the mechanical properties of cytoskeleton to rapidly and adaptively change. The present model provides a statistical mechanical underpinning for a tensegrity picture of the cytoskeleton.Rather than the traditional vector differential equation, this paper introduces rigid body dynamics in a new form, as a matrix differential equation. For a system of n(b) rigid bodies, the forces are characterized in terms of network theory, and the kinematics are characterized in terms of a directed graph of the connections of all members. The dynamics are characterized by a second order differential equation in a 3 x 2n(b) configuration matrix. The first contribution of the paper is the dynamic model of a broad class of systems of rigid bodies, characterized in a compact form, requiring no inversion of a variable mass matrix. The second contribution is the derivation of all equilibria as linear in the control variable. The third contribution is the derivation of a linear model of the system of rigid bodies. One significance of these equations is the exact characterization of the statics and dynamics of all class 1 tensegrity structures, where rigid bar lengths are constant and the string force densities are control variables. The form of the equations allow much easier integration of structure and control design since the control variables appear linearly. This is a significant help to the control design tasks.DThis paper focusses on shape changes of tensegrity structures. An optimization method is developed for design of a reference trajectory for shape changes of an arbitrary tensegrity structure. By defining an objective and constraints related to the shape change, constrained optimization is used to determine the reference trajectory. To improve suppression of vibrations during the shape change, an H2 controller is used in a feedback loop. To illustrate the use of the optimization method and selected control strategy, a shape change is simulated and the results are presented.?NOVELTY  A grid supporting membrane (312,314) has strips so that height of strip is less than half of the width to fasten strips to membrane. The strip has two elongated cords (311) and a polymer matrix (310) adhered to the cords. USE  Architectural element for covering infrastructure e.g. element of roof, air supported structure, suspended structure and tensegrity structure, for covering building infrastructure. ADVANTAGE  Enables to acquire a stronger, flexible strip. Prevents excessive stretching of the membrane due to weather conditions over long period of time.NNOVELTY  NOVELTY u Assembly holder for constructing a tensegrity structure before and during attachment of steel cable components (tension elements) to pressure rods of a support framework (14 assembly holders per pressure rod), especially for complex and large architectonic structures, compr< ises a geometric axis that simultaneously forms at each end of the assembly holder the normal of the axis of a pressure element and provides two skew pressure rods with the required support in the desired position with suitable connecting elements at exactly the geometric location at which the distance between the two pressure rods is the shortest. USE  USE u For constructing a tensegrity structure. ADVANTAGE  ADVANTAGE u The desired geometric position of the pressure rods can be held up to completion without additional steel cable components.This paper investigates the hypothesis that robots based on highly coupled mechanical structures can give rise to redundancy in control. Highly coupled mechanical structures have the property that actuation at one location can translate into movement at multiple locations, and conversely, movement at one location can be caused by multiple actuators. Due to this property, multiple control strategies may exist for a single behavior. Tensegrity structures which have recently been shown to form the basis for successful locomotor robots [8], have highly coupled mechanical structures. Thus, as a case study, it was of interest to investigate whether these new tensegrity based robots could offer a high degree of redundancy of control. This was investigated on two robots, based on three and four strut tensegrity prisms. Control strategies for locomotion were evolved using a genetic algorithm in simulation, and the evolved behaviors were compared. It was found that multiple control strategies existed for forward locomotion in both structures, and that qualitatively similar behavior could be obtained with significantly different control strategies. This indicated that a considerable degree of redundancy could exist in the control of robots based on highly coupled mechanical structures.nTensegrity structures are stable 3dimensional mechanical structures which maintain their form due to an intricate balance of forces between disjoint rigid elements and continuous tensile elements. Tensegrity structures can give rise to lightweight structures with high strengthtoweight ratios and their utility has been appreciated in architecture, engineering and recently robotics. However, the determination of connectivity patterns of the rigid and tensile elements which lead to stable tensegrity is challenging. Available methods are limited to the use of heuristic guidelines, hierarchical design based on known components, or mathematical methods which can explore only a subset of the space. This paper investigates the use of evolutionary algorithms in the formfinding of tensegrity structures. It is shown that an evolutionary algorithm can be used to explore the space of arbitrary tensegrity structures which axe difficult to design using other methods, and determine new, nonregular forms. It suggests that evolutionary algorithms can be used as the basis for a general design methodology for tensegrity structures.The computation of the equilibrium configurations of tensegrity mechanisms is often a very tedious task even for relatively simple architectures. However, it has been observed that the complexity of this problem is significantly reduced when gravitational loads are compensated with the use of static balancing techniques. In this work, the general static balancing conditions are adapted for the case of tensegrity mechanisms. Afterwards, the modified conditions are applied to two new spatial threedegreeoffreedom tensegrity mechanisms.Tensegrity structures have become of engineering interest in recent years, but very few have found practical use. This lack of integration is attributed to the lack of a well formulated design procedure. In this paper, a preliminary procedure is presented for developing morphing tensegrity structures that include actuating elements. To do this, the virtual work method has been modified to allow for individual actuation of struts and cables. A generalized connectivity matrix for a cantilever beam constructed from either a single 4strut cell or multiple 4strut cells has been developed. Global deflections resulting from actuation of specific elements have been calculated with or without external loads. Furthermore, the force density method is expanded to include a necessary upper bound condition such that a physically feasible structure can be designed. Finally, the importance of relative force density values on the overall shape of a structure comprising of multiple unit cells is discussed.IThis experimental study demonstrates the efficiency of simple control strategies to damp a 3stage tensegrity tower structure. The tower is mounted on a moving support which is excited with a limited bandwidth random signal (filtered white noise) by a shaker. Our goal is to minimize the transmissibility between base acceleration and top plate acceleration using piezoelectric displacement actuators and force sensors collocated at the bottom stage of vertical strings. Two types of controllers have been designed, namely, local integral force feedback control and acceleration feedback control. It can be shown that both controllers can effectively damp the first 2 bending modes by about 20 dB, and the acceleration feedback controller performs even better as it can also reduce the amplitude of the next 2 bending modes by about 510 dB.]The response to an external constraint of a symmetrical tensegrity structure made of elastic and rigid elements has been studied by numerical experiments. Two nonlinear effects have been found when the structure is close to its integrity limit above which it collapses. The first one is that the mechanical power response of the tensegrity structure can be modulated according to the magnitude of the applied force. This effect indicates that the structure may act as a mechanical power amplifier. The second one is that a slightly prestressed tensegrity structure can offer a greater resilience to an applied force than more prestressed equivalent structures. This paradoxical stiffening effect indicates that increasing the prestress may not always be the most efficient way to keep the stability of the structure. (C) 2004 Elsevier Ltd. All rights reserved.During the design of mechanical systems one normally exploits numerical analysis and optimization tools. We make a plea for symbolic computation and give an example where structural displacements under load are computed symbolically. Geometrical design parameters enter in this computation. The set of equilibrium conditions, linear in the displacements, but nonlinear in the design parameters, is solved symbolically. The resulting expressions reveal the geometry which yield optimal properties for stiffness or stiffnesstomass. This technique is applied to a class of repetitive mechanical systems, namely tensegrity structures. A large scale example with 1533 degreesoffreedom is computed successfully. The results make it possible to optimize the structure with respect to stiffness properties, not only by appropriately selecting (continuous) design parameters, influencing geometry, but also by selecting the number of stages used to build up the structure (a discrete design parameter), influencing topology.Most active structures involve direct control of single parameters when there is a closed form relationship between the response required and the control parameter. Building on a previous study of an adjustable structure, this paper describes geometric active control of a reusable tensegrity structure that has been enlarged to five modules with improved connections and is equipped with actuators. Closely coupled strut and cable elements behave nonlinearly (geometrically) even for small movement of the 10 telescopic struts. The control criterion for maintaining the upper surface slope has no closed form relationship with strut movement. The behavior of the structure is studied under 25 load cases. A newly developed stochastic search algorithm successfully identifies good control commands following computation times of up to I It. Sequential application of the commands through sets of partial commands helps to avoid exceeding limits during < intermediate stages and adds robustness to the system. Reuse of a previously calculated command reduces the response time to less than 1 min. Feasible storage and reuse of such commands confirm the potential for improving performance during service.aThis paper concerns the optimal masstostiffness ratio design of class2 tensegrity towers. For different loading scenarios, the procedure seeks the topology and geometry of the structure that yields an optimal design satisfying common constraints. The domain of feasible tenseuritv eometries is defined by imposing tensegrity equilibrium conditions on both unloaded and loaded structure. Remainin constraints include strength constraints for all elements of the structure and buckling constraints for bars. The symmetry of the design is imposed by restricting the domain of geometric variables and element parameters. The static response of the structure is computed by using a nonlinear large displacement model. The problem is cast in the form of a nonlinear proram. The influence of material parameters on the optimal shape of the structure is investigated.This paper concerns openloop control laws for reconfiguration of tensegrity towers. By postulating the control strategy, as an equilibrium tracking control, very little control energy is required. Several different reconfiguration scenarios are possible for different string connectivity schemes. This includes unit radius control, twist angle control and truncation parameter control. All these control laws allow a nonuniform distribution of the control parameters among units. By defining a wavelike reference signal and injecting it in the openloop control law, we demonstrate the concept of selfpropelled tensegrity structure that are capable of locomotion.lTensegrity structures are special truss structures composed of bars in compression and cables in tension. Most tensegrity structures under investigation, to date, have been of Class 1, where bars do not touch. In this article, however, we demonstrate the hardware implementation of a 2 stage symmetric Class 2 tensegrity structure, where bars do connect to each other at a pivot. The open loop control law for tendon lengths to accomplish the desired geometric reconfiguration are computed analytically. The velocity of the structure's height is chosen and reconfiguration is accomplished in a quasistatic manner, ignoring dynamic effects. The main goal of this research was to design, build. and test the capabilities of the Class 2 structure for deployment concepts and to further explore the possibilities of multiple stage structures using the same design and components.This paper investigates the local uniqueness of designs of mcircles ( lines and circles) in the plane up to inversion under a set of angles of intersection as constraints. This local behavior is studied through the Jacobian of the angle measurements in a form analogous to the rigidity matrix for a framework of points with distance constraints. After showing directly that the complete set of angle constraints on v distinct mcircles gives a matrix of rank 3v  6, we show that the Jacobian is column equivalent by a geometric correspondence to the rigidity matrix for a barandjoint framework in Euclidean 3space. As a corollary, the complexity of the independence of angle constraints on generic plane circles is the complexity of the old unsolved combinatorial problem of generic rigidity in 3space. This theory is not known to have a polynomial time algorithm for generic independence that offers a warning about the complexity of general systems of geometric constraints even in the plane. Our correspondence extends to all dimensions. Angle constraints on spheres in 3space then match the even more complex firstorder theory of frameworks in 4space. This theory is not predicted to have a polynomial time algorithm for generic points.A systematic design method is proposed for the selecting of actuators and sensors in the structural control in order to minimize the instrumental cost. With actuators and sensors placed at all the admissible locations initially, an iterative minimization algorithm is carried out to identify the sensor/actuator that requires the least precision. By deleting the roughest sensor/actuator each time till loss of feasibility, one can conclude simultaneously the necessary number and type of sensor/actuator, and the location and precision for each sensor/actuator. A tensegrity structure example has been solved as an application of the proposed algorithm.QTensegrity structures represent a special class of flexible structures, whose members can simultaneously perform the functions of strength, sensing, actuating, and feedback control. In this article we show how these structures intrinsic properties can be exploited to construct a smart sensor for simultaneous measurement of six different quantities: three orthogonal forces and three orthogonal torques. The static and dynamic characteristics of the sensor are computed and the influence of friction and prestress upon these characteristics is analyzed. An optimal estimator design is presented and its performance is evaluated through numerical simulations. These simulations indicate that the tensegrity sensor is capable of simultaneously providing correct estimates of the six quantities of interest. (C) 2004 Elsevier B.V. All rights reserved.NOVELTY  Twelve covers are shaped to individually cover twelve pentagonal openings. Each cover is attached so as to form an airtight seal. The twenty intersections of six bands are covered and/or sealed to form an airtight seal. The seams of the enclosure are sealed to make the enclosure airtight. USE  Used as e.g. building, pressure vessel, vacuum vessel, liquid or gas container. ADVANTAGE  Shortens construction time, and reduces construction cost. Increases weighttostrength ratio, and avoids rolling away. DETAILED DESCRIPTION  INDEPENDENT CLAIMS are also included for the following: (A) a dodecahedral framework and spherical structure combination; (B) a spherical dodecahedron and tensegrity dodecahedron combination; and (C) a tower utilization method.dNOVELTY  The joint (1) has a main body (4) connected to the tips of several rods (2) that can be tilted. The joint main body connects each rod, such that the tilting center of each rod is positioned on a circular track. A connection rod (3) is arranged at the central point of the circular track, such that the rods can be tilted with respect to the connection rod. USE  For use in a foldable tensegrity structure. ADVANTAGE  Prevents connected rods from being obstructive to ensure smooth and compact folding of tensegrity structure. Ensures efficient assembly and convenient folding of tensegrity structure._This paper presents a closedform analysis of a twospring planar tensegrity mechanism to determine all possible equilibrium configurations for the device when no external forces or moments are applied. The equilibrium position is determined by identifying the configurations at which the potential energy stored in the two springs is a minimum. A 28th degree polynomial expressed in terms of the length of one of the springs is developed where this polynomial identifies the cases where the change in potential energy with respect to a change in the spring length is zero. A numerical example is presented.jUncertain environments stimulate development of innovative structures. Structures that can adapt to new environments and improve their performance over time have much potential for meeting new challenges. This paper reports on the construction of a unique active tensegrity structure containing five modules and ten actuators on telescopic bars in a closely coupled configuration. The control scenario under study is a constant slope requirement for quasistatic control. Behaviour is geometrically nonlinear and this is modelled using a combination of dynamic relaxation analysis with a neuralnetwork based correction to account for effects such as joint friction. There is no direct solution for bar movements given required slope. Furthermore, the entire search space is very large. A standard < engineering brutforce methodology of generate, analyse and test could take up to 10(22) years to find a control solution. A stochastic search method reduces search time down to approximately one hour. Case based reasoning with stochastic search for case adaptation reduces search time further down to tens of seconds. Adding cases allows the structure to learn from its experience. An initial study of self diagnosis and self repair reveals that there is potential for demonstrating greater autonomy, thereby increasing the ability of the structure to accommodate uncertain environments.?For a new class of tendondriven robotic systems that is generalized to include tensegrity structures. this paper focuses on a method to jointly optimize the control law and the structural complexity for a given pointtopoint maneuvering task. By fixing external geometry, the number of identical stages within the domain is varied until a minimal mass design is achieved. For the deployment phase, a new method is introduced which determines the tendon force inputs from a set of admissible. nonsaturating inputs, that will reconfigure each kinematically invertible unit along its own path in minimum time. The approach utilizes the existence conditions and solution of a linear algebra problem that describe how the set of admissible tendon forces is mapped onto the set of pathdependent torques. Since this mapping is not onetoone, free parameters in the control law always exist. An infinitynorm minimization with respect to these free parameters is responsible for saturation avoidance. In addition to the required time to deploy the expended control energy during the postmovement phase is also minimized with respect to the total number of stages. Conditions under which these independent minimizations yield the same robot illustrate the importance of considering control/structure interaction within this new robotics paradigm.For a new class of tendondriven robotic systems that is generalized to include tensegrity structures, this paper focuses on a method to determine the tendon force inputs from a set of admissible, nonsaturating inputs, that will move the rigidbody system from point A to point B along a prescribed path in minimum time. The approach utilizes the existence conditions and solution of a linear algebra problem that describes how the set of admissible tendon forces is mapped onto the set of pathdependent torques. Since this mapping is not onetoone, free parameters in the control law always exist. An infinitynorm minimization with respect to these free parameters is responsible for saturation avoidance. Characterizing and optimizing th
!"#$%&'()*+,./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdeghijklmnopqrstuvwxyz{}~ese free parameters is the new contribution. Feedback is introduced to attenuate disturbances arising from the tensegrity paradigm. Examples illustrate methods and validate tensegrity's superior saturation avoidance capability.rConsider a planar linkage, consisting of disjoint polygonal arcs and cycles of rigid bars joined at incident endpoints (polygonal chains), with the property that no cycle surrounds another arc or cycle. We prove that the linkage can be continuously moved so that the arcs become straight, the cycles become convex, and no bars cross while preserving the bar lengths. Furthermore, our motion is piecewisedifferentiable, does not decrease the distance between any pair of vertices, and preserves any symmetry present in the initial configuration. In particular, this result settles the wellstudied carpenter's rule conjecture.This paper demonstrates that symmetric tensegrity structures can have a shape memory effect. It has been found that the ratio of potential energy between two equilibrium states can vary considerably when the original length of the elastic elements is changed. It is then suggested that those structures may be used as shape memory actuators. (C) 2003 Elsevier Science Ltd. All rights reserved.Many engineering tasks involve the search for good solutions among many possibilities. In most cases, tasks are too complex to be modeled completely and their solution spaces often contain local minima. Therefore, classical optimization techniques cannot, in general, be applied effectively. This paper studies two stochastic search methods, one wellestablished (simulated annealing) and one recently developed (probabilistic global search Lausanne), applied to structural shape control. Search results are applied to control the quasistatic displacement of a tensegrity structure with multiple objectives and interdependent actuator effects. The best, method depends on the accuracy related to requirements defined by the objective function and the maximum number of evaluations that are allowed.Structural analyses of tensegrity structures must account for geometrical nonlinearity. The dynamic relaxation method correctly models static behavior in most situations. However, the requirements for precision increase when these structures are actively controlled. This paper describes the use of neural networks to improve the accuracy of the dynamic relaxation method in order to correspond more closely to data measured from a fullscale laboratory structure. An additional investigation evaluates training the network during the service life for further increases in accuracy. Tests showed that artificial neural networks increased model accuracy when used with the dynamic relaxation method. Replacing the dynamic relaxation method completely by a neural network did not provide satisfactory results. First tests involving training the neural net work online showed potential to adapt the model to changes during the service life of the structure.A tensegrity is a lightweight space structure consisting of compression members surrounded by a network of tension members. They can be easily dismantled and therefore provide innovative possibilities for reusable and modular structures. Tensegrities can adapt their shape by changing their self stress, and when equipped with sensors and actuators, they can adapt to changing environments. A fullscale prototype of an adjustable tensegrity has been built and tested at Swiss Federal Institute of Technology (EPFL). This paper begins with a description of important aspects of the design, assembly, and static testing. Tests show that the structure behaves linearly when subjected to vertical loads applied to a single joint. Nonlinearities are detected for small displacements, for loads applied to several joints and for adjusting combinations of telescoping compression members. To predict behavior, dynamic relaxationa nonlinear methodhas been found to be reliable. Appropriate strut adjustments found by a stochastic search algorithm are identified for the control goal of constant roof slope and for the load conditions studied. When adjusting struts, an excessive number of adjustable members does not necessarily lead to improved performance.Evanescent waveexcited fluorescence microscopy, which selectively probes the ventral membranes of cells adhered to glass substrate, was utilized to observe the change in the topography of the ventral plasma membranes of Swiss 3T3 fibroblasts during spreading. In the initial stage of the spreading (up to 2 hours after seeding), the ventral membrane was close (<100 nm) to the substrate in the peripheral and the central regions. About 4 hrs after seeding, the ventral surface assumed a flat topography for a short period and then gradually became uneven, displaying streak pattern of celltosubstrate contact (6  8 hours after seeding). By 24 hours after seeding, cells gained polygonal shape and most regions except for the focal adhesions were separated from the substrate. Within these wellspread cells actin stress fibers were found to emanate obliquely from the focal adhesions, as previously reported. When cells were grown in the presence of 2,3butanedione monoxime (BDM), an inhibitor of actomyosinbased contraction of stress fibers and the cell, the ventral membranes in majority of the cells displayed flat topography, and the tilt of the stress fibers decreased. Cells grown in the presence of colchicine, a microtubuledepolymerizing agent also possessed < flat ventral membrane and less tilted stress fibers. These results suggest that the contraction of stress fibers and integrity of microtubules are important in the formation of the uneven topography of ventral membrane and the tilt of, stress fibers.dThe aim of this paper is to present a possible developline for the study of large lightweight roof structures by nonlinear geometric analysis, under the dynamic effects of the turbulent action of the wind, that can be applied into the classical engineering applications. In particular the paper deals with the study of tensegrity systems, that can be defined as pattern that results when push (struts) and pull (tendons) have a winwin relationship with each other. The pull is continuous and the push is discontinuous. The continuous pull is balanced by the discontinuous push producing an integrity of tensioncompression. Static and dynamic analyses of the wind action effects on one example of such tensegrity system, i.e. the roof over the La Plata stadium, Argentina, have been performed by using the geometrically nonlinear FE procedure named "Loki". The wind loads are simulated as deformationdependent forces. Both experimental data and numerical results available from the roof designers, have permitted to control the reliability of the proposed mathematical model. (C) 2003 Elsevier Ltd. All rights reserved.iIn this project. we have designed a new type of flexible surface. which we call a tensegrity fabric. and simulated the interaction of this flexible surface with a nearwall turbulent flow. The fabric is constructed by weaving together both members in tension (tendons) and members in compression (bars) to form a plateclass tensegrity structure, then covering this discrete flexible structure with a continuous flexible membrane. We have modeled the flow/structure interaction by coupling a spectral Direct Numerical Simulation (DNS) code resolving the (continuous) turbulent flow system and an efficient structural dynamics code which simulates directly the motion of the (discrete) extensive, smallscale, and interconnected tensegrity structure. The structural dynamics code used was developed by Prof. Robert Skelton's lab at UC San Diego. An immersed boundary method is used to capture the effect of the moving boundary in the DNS, and a simple tessellation strategy is used to lump the distributed fluid forces (skin friction and pressure) acting on the membrane onto the nearby nodes of the tensegrity structure. Our ultimate goal is to use this new simulation tool to optimize the design of the tensegrity structure (specifically, the orientation, stiffness, mass, and damping of each of the individual tendons and bars in the unit cell upon which the tensegrity structure is based). Our objective in this optimization is to tune the compliance properties of the fabric in such a way as to reduce the skinfriction drag induced at the flow/structure interface by weakening the vortices near the wall in the overlying turbulent flow.Tensegrity structures consist of tendons (in tension) and bars (in compression). Tendons are strong, light, and foldable, so tensegrity structures have the potential to be light but strong and deployable. Pulleys NiTi wire, or other actuators to selectively tighten some strings on a tensegrity structure can be used to control its shape. This article describes the problem of asymmetric reconfiguration of tensegrity structures and poses one method of finding the open loop control law for tendon lengths to accomplish the desired geometric reconfiguration. In addition, a practical hardware experiment displays the readiness and feasibility of the method to accomplish shape control of the structure.Tensegrity systems are innovative strut and cable systems used in Civil Engineering. Their lightness and the impression of transparency they convey represent new sources of inspiration for architects. Nevertheless, their conception and their design are not easy insofar as these systems are reticulate, spatial and selfstressed. In this article we set out to present the different stages of the conception and the design of tensegrity systems. The study of the selfstress, the choice of its level, the design of the elements and the study of the sensitivity to manufacturing element errors are the different subjects described. We will then present the concrete case of a double layer grid of 81 m(2) area. (C) 2003 Elsevier Science Ltd. All rights reserved.In this paper we present a strategy for tensegrity structures deployment. The main idea is to use a certain set of equilibria to which the undeployed and deployed configurations belong. In the state space this set is represented by an equilibrium manifold. The deployment is conducted such that the deployment trajectory is close to this equilibrium manifold. (C) 2003 Elsevier Ltd. All rights reserved.A general class of tensegrity structures, consisting of both compression members, that is, bars, and tensile members, that is, cables, is defined. For a given number N of bars, we define the topological structure that is necessary to establish a tensegrity. Necessary and sufficient conditions for prestress mechanical equilibria of the tensegrity are then provided in terms of a nonlinear function of the position and orientation of the bars and the rest lengths of the cables.This paper characterizes the necessary and sufficient conditions for tensegrity equilibria. Static models of tensegrity structures are reduced to linear algebra problems, after first characterizing the problem in a vector space where direction cosines are not needed. This is possible by describing the components of all member vectors. While our approach enlarges (by a factor of 3) the vector space required to describe the problem, the advantage of enlarging the vector space makes the mathematical structure of the problem amenable to linear algebra treatment. Using the linear algebraic techniques, many variables are eliminated from the final existence equations. (C) 2003 Elsevier Ltd. All rights reserved.A new topology for a prestressed tensegrity plate, the unstableunit tensegrity plate (UUTP), is introduced, together with a detailed algorithm for its design. The plate is a truss made of strings (flexible elements) and bars (rigid elements), which are loaded in tension and compression, respectively, where bars do not touch each other. Given the outline dimensions of the desired plate, and the number of bars along the plate's width and length, the algorithm solves for the nodes' positions and the prestress forces that make a plate in equilibrium. This is done by solving a nonlinear matrix equation via Newton's method. This equation reflects static equilibrium conditions. We've designed several such plates, proving the feasibility of the proposed topology and the effectiveness of its design algorithm. Two such plates are characterized in detail, both statically and dynamically (via simulation). The proposed algorithm may be extended to solve for other tensegrity structures having different topologies and/or different shapes. The UUTP may be used as a building block of many types of structures, both uncontrolled and controlled, either largescale or miniaturescale.NOVELTY  A bracket (60) has an elongated opening with a large diameter portion and a small diameter portion which respectively allow a stopper of a continuous tension cable (45) to pass through and inhibits passage of the stopper. USE  For tensegrity structure e.g. dome, tower. ADVANTAGE  Enables easy and rapid deployment without altering the length of the tension cables. Prevents entangling of tension cable in collapsed state of the tensegrity unit by holding the cables in attached state. The tensegrity unit is sturdy, durable, lightweight, simple, safe, inexpensive, efficient, versatile, ecologically compatible, energy conserving reliable and is easy to assemble, install and use. DETAILED DESCRIPTION  INDEPENDENT CLAIMS are included for the following: (1) Tensegrity structure; (2) Method of constructing tensegrity structure; (3) Method of forming a tensegrity unit; and (4) Tensegrity unit structure coupling mechanism.< Special structures are landmarks and testimonials to the achievements of the structural engineering profession. They are true threedimensional representations of our equilibrium equations and affirmations of our analytical techniques, design standards and construction practices. They include many types of structures, such as: space frames or grids; cableandstrut and tensegrity; airsupported or airinflated; selferecting and deployable; cable net; tension membrane; lightweight geodesic domes; folded plates; and thin shells. This work celebrates the ASCE's sesquicentennial by providing a historical perspective on how special structures have evolved, their stateofpractice in the dawn of the 21st century, and a projection of their potential trends and evolution into the future.Tensegrity is a light weight deployable structure that is composed of compressive and tensile members. However, the compressive members, which are made of common metallic structural materials, are not massefficient. In this paper, we replace the compressive member with selfsimilar tensegrity structure that has same strength but less mass. We start with a nontensegrity structure called C4T1(i) and show that it can be designed to have the same strength but less weight compared with the compressive member to be replaced. The stiffnesstomass ratio of the C4T1(i) structure, however, is compromised. We then modify the C4T1(i) structure to a tensegrity structure called C4T2(i) by adding another set of string(s) with prestress. It can be shown that C4T2(i) is a better substitute of the compressive members in a structure because of less mass and same strength but higher stiffnesstomass ratio.A tensegrity structure is built using compressive members (bars) and tensile members (tendons). We discuss how an optimal and integrated design of tendon length control and topology/geometry of the structure can improve the stiffness and stiffnesstomass properties of tensegrity systems. To illustrate our approach we apply it on a tensegrity system build up from several elementary stages that form a planar beam structure. The computations are done with a nonlinear programming approach and most design aspects (decentralized colocated control, static equilibrium, yield and buckling limits, force directionality, etc., both for the unloaded and loaded cases) are incorporated. Due to the way the control coefficients are constrained, this approach also delivers information for a proper choice of actuator or sensor locations: there is no need to control or sense the lengths of all tendons. From this work it becomes clear that certain actuator/sensor locations and certain topologies are clearly advantageous. For the minimal compliance objective in a planar tensegrity beam structure, proper tendons for control are those that are perpendicular to the disturbance force direction, close to the support, and relatively long, while good topologies are the ones that combine different nodal configurations in a tensegrity topology that is akin to a framed beam, but, when control is used, can be quite different from a classical truss structure. Geometrically nonlinear analyses are used to study the static structural behavior of three cable systems. All analyses and results are nondimensional and therefore valid for any scale. The behavior of a system that has a singular linear stiffness matrix is compared to that of a comparable system that has a nonsingular linear stiffness matrix. The actions considered include pretensioning, uniform dead load, asymmetric and antisymmetric vertical live loads and moving vertical live loads. There is no distinct improved static behavior associated with the system that has a nonsingular linear stiffness matrix. The nonlinear behavior of a cable stiffened by a girder is also studied. The behavior of the deckstiffened system depends strongly on a nondimensional parameter defined by the moment of inertia of the girder divided by the area of the suspension cable times the square of its sag. A preliminary comparison of the relative effectiveness of stiffening with a girder versus stiffening by longitudinal pretensioning is made.Over the past two decades, significant information has become available that reveals the fundamental role of mechanical factors in controlling the complex structure and function of many cell types. There is a pressing need, however, to synthesize these many observations via mathematical models, which have predictive capability and which suggest experiments that will provide increased insight and thus refinement of the models. In this paper, it is suggested that some of the salient mechanical behaviors exhibited by cells, including dynamic mechanosensitive changes therein, can be described using a simple constrained mixture model that has recently been proposed for describing tissuelevel growth and remodeling. That is, strong similarities in structurefunction relationships at multiple length scalescell, tissue, and organmay allow us to exploit common constitutive frameworks, which may prove advantageous in future attempts to model across the various scales.The method of constrained particle dynamics is used to develop a dynamic model of order 12N for a general class of tensegrity structures consisting of N compression members (i.e. bars) and tensile members (i.e. cables). This model is then used as the basis for the design of a feedback control system which adjusts the lengths of the bars to regulate the shape of the structure with respect to a given equilibrium shape. A detailed design is provided for a 3bar structure.We studied the relation between actin structural changes and cytoskeleton mechanical properties in living adherent epithelial alveolar cells, before and during actin depolymerization. The mechanical response of adherent alveolar epithelial cells was measured using magnetic twisting cytometry and a twocomponent model representing the cortical and cytosolic elastic components at equilibrium. Chemiluminescent staining of the actin cytoskeleton was performed in the same living cells to estimate the intracellular actin density distribution for each cytoskeleton component. We found that (i) cytoskeleton alterations induced by actin depolymerization differed between the cortical and cytosolic cytoskeleton components (e.g., 30% and 49%, respectively, at a stress of 31 Pa) and that (ii) the concomitant change in actin distribution was also different (e.g., actin volume decrease was 7% and 19% for the cortical and cytosolic components, respectively).nOne of the main properties of tensegrity structures, that sets them apart from most of structures, is that they are vary suitable for shape control. This can be accomplished by controlling lengths of string members. Tensegrity deployment is considered herein as a tracking control problem. Therefore, the required trajectories should be feasible for a given structure. For tensegrity structures, this means that in every desired configuration, the structure has to satisfy tensegrity conditions, which require strings to be in tension, and the structure to be stable. To define an openloop deployment control law, geometry parameterization of those configurations and corresponding rest lengths of string elements guaranteeing equilibrium are defined first. By slowly varying desired geometry, an openloop string rest length control is defined. This makes the structure track trajectories defined by the time dependent geometry parameters. Two examples are illustrated: 1) Deployment of planar tensegrity beams made of symmetric stable tensegrity units, 2) Deployment of plates made of stable symmetric shell class tensegrity units.<Many papers have mentioned deployability as the advantage of the tensegrity structures. This paper proposes an openloop control law for the deployment of a platelike structure. The control law is decentralized so that each stable unit is given the same control commands. The second contribution of this paper is the design of a deployable tensegrity plate composed of stable units connected in a special manner that yields a stable overall system without control. Very few str< uctures are stable in the absence of control and also controllable to a different equilibrium.We improved the force modulation mode with scanning probe microscopy (SPM) in order to make a quantitative evaluation of the viscoelasticity of living cells. Taking account of the viscosity of liquid medium, the vibration frequency of the cantilever was selected to be 500 Hz, and analysis of cantilever vibration was adopted for evaluation of the viscoelasticity of the samples. Consequently, we have succeeded in determining viscoelasticity distribution on living cells. The values of Young's modulus and the coefficient of viscosity vary from 10 to 50 kPa and from 20 to 40 Pa(.)s on a cell, depending on its internal cellular structure.Since structural control of civil structures was first proposed in 1972, most research and applications have focused on enhancing the safety of structures under extreme conditions. This paper introduces a new direction in structural control: the use of computational methods and explicitly defined knowledge to improve serviceability and maintenance of civil structures. The objectives of such structures, called intelligent structures, are to maintain and improve structural performance by recognizing changes in behaviors and loads, adapting the structural geometry to meet defined goals, and using past events to improve future performance. A computational framework based on intelligent control methodology is presented that combines reasoning from explicit knowledge, search, learning and planning to illustrate a vision for intelligently controlled civil structures. This is applied to enable global shape control of an adjustable tensegrity structure using a combination of simulated annealing search, dynamic relaxation analysis and structural measurements. Active tensegrity structures are modular, reusable cable structures that do not require expensive anchorages or steep slopes. This provides an innovative solution for temporary structures. Particularly, when used for exhibitions, they could become part of an exhibition, rather than just house one. As part of a multistage project, results presented in this paper demonstrate the feasibility of building an intelligent tensegrity structure. (C) 2002 Elsevier Science Ltd. All rights reserved.&Static models of tensegrity structures are reduced to linear algebra problems, after first characterizing the problem in a vector space where direction cosines are not needed. That is, we describe the components of all member vectors as opposed to the usual practice of characterizing the statics problem in terms of the magnitude of tension vectors. While our approach enlarges (by a factor of 3) the vector space required to describe the problem, the computational space is not increased. The advantage of enlarging the vector space makes the mathematical structure of the problem amenable to linear algebra treatment. Using the linear algebraic techniques, many variables are eliminated from the Final existence equations. This paper characterizes the existence conditions for all tensegrity equilibria.The linearized equations of motion for tensegrity structures around arbitrary equilibrium configurations are derived. For certain tensegrity structures which yield particular equilibrium configurations of practical interest, the linearized models of their dynamics around these configurations are presented. Evidence which indicates that these equilibria are stable is given and some stiffness and dynamic properties of these structures are investigated. (C) 2002 Elsevier Science Ltd. All rights reserved.In this article we first present a mathematical model which describes the nonlinear dynamics of tensegrity structures. For certain tensegrity structures a particular class of motions, coined symmetrical motions, is defined. The corresponding equations of motion are derived and the conditions under which symmetrical motions occur are established. Reconfiguration procedures through symmetrical motions are proposed and examples are given. (C) 2002 Elsevier Science Ltd. All rights reserved.Future small satellite missions require lowcost, precision reflector structures with large aperture that can be packaged in a small envelope. Existing furlable reflectors form a compact package which, although narrow, is too tall for many applications. An alternative approach is proposed, consisting of a deployable "tensegrity" prism forming a ring structure that deploys two identical cable nets (front and rear nets) interconnected by tension ties; the reflecting mesh is attached to the front net. The geometric configuration of the structure has been optimized to reduce the compression in the struts of the tensegrity prism. A smallscale physical model has been constructed to demonstrate the proposed concept. A preliminary design of a 3mdiam, 10GHz reflector with a focallengthtodiameter ratio of 0.4 that can be packaged within an envelope of 0.1 x 0.2 x 0.8 m(3) is presented.{A new type of parallel mechanism is introduced that is based on the principle of tensegrity. In tensegrity structures, ties are used for elements that are in tension and struts for elements that are in compression. In this paper, three of the ties of a tensegrity structure are comprised of a compliant and a noncompliant segment that are in series. The length of the three noncompliant segments can be varied in order to control the shape and desired compliant characteristics of the tensegrity mechanism. This paper will describe the new mechanism in detail and present a reverse displacement and compliance analysis of the device.The cable dome, proposed by Geiger after developing Fuller's idea of tensegrity, is a new type of space structure. This paper is concerned with the nonlinear analysis and the optimum design of cable domes. In the first part of the paper, a specific equilibrium state named integral feasible prestress is proposed and determined. Then a twonode curved cable element is presented and the nonlinear analysis of the static behaviour of cable domes is performed on the basis of the available integral feasible prestress state. The optimum design of cable domes is studied in the third part. Two optimal variables, including prestress level and cross stress, are considered respectively. And the corresponding algorithms are also developed. The numerical results of illustrative examples show the accuracy and validity of the nonlinear analysis model and the optimum algorithms. The work presented here is very useful for understanding the behaviour of cable domes. (C) 2002 Elsevier Science Ltd. All rights reserved.This paper considers a class of tensegrity structures with continuous tubular compression booms forming curved splines, which may be deployed from straight by prestressing a cable bracing system. A freeform arch structure for the support of prestressed membranes is reviewed and the concepts are extended to a twoway spanning system for double layer grid shell structures. A numerical analysis based on the Dynamic Relaxation (DR) method is developed which caters specifically for the formfinding and load analysis of this type of structure; a particular feature of the analysis is that bending components are treated in a finite difference form with three degrees of freedom per node rather than six. This simplifies the treatment of sliding collar nodes which may be used along the continuous compression booms of deployable systems. (C) 2000 Elsevier Science Ltd and CivilComp Ltd. All rights reserved.We introduce a new class of bootstrap percolation models where the local rules are of a geometric nature as opposed to simple counts of standard bootstrap percolation. Our geometric bootstrap percolation comes from rigidity theory and convex geometry. We outline two percolation models: a Poisson model and a lattice model. Our Poisson model describes how defectsholes is one of the possible interpretations of these defectsimposed on a tensed membrane result in a redistribution or loss of tension in this membrane; the lattice model is motivated by applications of Hooke spring networks to problems in material sciences. An analysis of the Po< isson model is given by Menshikov et al.((4)) In the discrete setup we consider regular and generic triangular lattices on the plane where each bond is removed with probability lp. The problem of the existence of tension on such lattice is solved by reducing it to a bootstrap percolation model where the set of local rules follows from the geometry of stresses. We show that both regular and perturbed lattices cannot support tension for any p < 1. Moreover, the complete relaxation of tension as defined in Section 4occurs in a finite time almost surely. Furthermore, we underline striking similarities in the properties of the Poisson and lattice models.A systematic method of selecting sensors and actuators is produced, efficiently selecting inputs and outputs that guarantee a desired level of performance in the H.norm sense. The method employs an efficiently computable necessary and sufficient existence condition, using an effective search strategy. The search strategy is based on a method to generate all socalled minimal dependent sets. This method is applied to tensegrity structures. Tensegrity structures are a prime example for application of techniques that address structural problems, because they offer a lot of flexibility in choosing actuators/sensors and in choosing their mechanical structure. The selection method is demonstrated with results for a 3 stage planar tensegrity structure where all 26 tendons can be used as control device, be it actuator, sensor, or both, making up 52 devices from which to choose. In our setup it is easy to require devices to be selected as colocated pairs, and to analyze the performance penalty associated with this restriction. Two performance criteria were explored, one is related to the dynamical stiffness of the structure, the other to vibration isolation. The optimal combinations of sensors and actuators depend on the design specifications and are really different for both performance criteria.~A set of procedures was presented for characterizing static and dynamic response of tensegrity modules. The procedures were applied to two tensegrity modules: a shbal spherical module and a twostage cylindrical module with three bars at each stage. The singular value decomposition of the initial equilibrium matrix revealed prestress and infinitesimal mechanism modes. The prestress stiffening effect of infinitesimal mechanism modes was found to be isotropic at each node. In the initial quasistatic loaning, infinitesimal mechanisms exhibited soft response. As the deformation advanced the stiffness of tensegirty modules increased almost quadratically with infinitesimal mechanism amplitudes, Modal analyses revealed that the lowest modes were those of infinitesimal mechanism modes and their natural frequencies were an order of magnitude smaller than those of higher deformation modes.Initial equilibrium and modal analyses of cyclic rightcylindrical tensegrity modules with an arbitrary number of stages are presented. There are m (greater than or equal to 3) bars at each stage. The Maxwell number of the modules is 6  2m and is independent of the number of stages in the axial direction. Calladine's relation reveals that there are 2m  5 infinitesimal mechanism modes. For multistage modules the necessary conditions for axial assembly of onestage interior modules with the same internal element forces are investigated. Onestage modules with either congruent rightcylindrical modules or geometrically similar coneshaped modules satisfy the necessary conditions. In this paper, the axial assembly of rightcylindrical modules with flip or quasiflip symmetry is considered. For prestressed configurations, modal analyses are conducted to investigate the mode shapes of infinitesimal mechanism modes. (C) 2001 Elsevier Science Ltd. All rights reserved.In order to present basic equations for static and dynamic analyses of a class of truss structures called tensegrity structures, largedeformation kinematics and kinetics were presented in both Eulerian and Lagrangian formulations. The two sets of equations of motion yield the same values even if different stress and strain measures were employed for their computation. The Eulerian formulation was implemented in an updated Lagrangian finite element code using Newton's method with consistently linearized equations of motion. By utilizing the linearized Lagrangian equations of motion at prestressed initial configurations, harmonic modal analyses of a threebar tensegrity module and a sixstage tensegrity beam were conducted. In the second part of the paper, linearized equations were utilized to investigate the equilibrium configurations of basic tensegrity modules and the stiffness of prestressed tensegirty structures. (C) 2001 Elsevier Science Ltd. All rights reserved.BLinearized Lagrangian equations developed in the first part of the paper were employed for static analyses of cyclic cylindrical tensegrity modules. Linearized equilibrium equations at natural configurations were used to investigate initial shape, static and kinematic indeterminancy, prestress and infinitesimal mechanism modes, and the sensitivity analysis of initial geometry. Linearized equilibrium equations at prestressed initial configurations were utilized to investigate prestress stiffening and to distinguish firstorder mechanisms from higherorder mechanisms. To estimate critical loads for bar buckling and cable slacking, nonlinear equilibrium equations were employed to compute element forces. Further, the equivalence between the twist angle theorem obtained from a geometrical consideration and the equilibrium analysis was established for cyclic cylindrical tensegrity modules. It is concluded that infinitesimal mechanism modes and prestresses characterize the static and dynamic response of tensegrity structures. (C) 2001 Elsevier Science Ltd. All rights reserved.*Static and dynamic properties of a pair of dual spherical tensegrity modules invented by Buckminster Fuller are investigated. They are regular truncated icosahedral and dodecahedral tensegrity modules. The computation of the Maxwell number and the use of Calladine's relation reveal that regular truncated icosahedral and dodecahedral tensegrity modules possess 55 infinitesimal mechanism modes. A reduced equilibrium matrix is presented for the initial shape finding to economically impose the existence of a prestress mode. Both the initial shape and the corresponding prestress mode are analytically obtained by using graphs of the icosahedral group and the reduced equilibrium matrix. For both icosahedral and dodecahedral modules the maximum values of the cable tension is always less than the absolute value of bar compression. In order to classify a large number of infinitesimal mechanism modes, modal analyses are conducted. Infinitesimal mechanism modes have the stiffness due to prestress and are associated with lowest natural frequencies. Their natural frequencies increase proportionally to the square root of the amplitude of prestress. It is found that there are only 15 distinct natural frequencies associated with the infinitesimal mechanism modes. (C) 2001 Elsevier Science Ltd. All rights reserved.1Initial equilibrium and modal analyses of Kenneth Snelson's cyclic frustum tensegrity modules with an arbitrary number of stages are presented. There are m (greater than or equal to3) bars at each stage. The Maxwell number of the modules is 6  2m and is independent of the number of stages in the axial direction. Calladine's relations reveals that there are 2  5m infinitesimal mechanism modes, For multistage modules the necessary conditions for axial assembly of onestage modules with the same internal elementforces are investigated. Onestage modules with geometrically similar frustum modules satisfy the necessary conditions. For prestressed configurations, modal analyses were conducted to investigate the mode shapes of infinitesimal mechanism modes, (C) 2001 Elsevier Science B.V. All rights reserved.The most interesting examples of tensegrity structures are underconstrained and display an infinitesimal flex. In the direction of that flex t< he forcedisplacement relationship is highly nonlinear, resulting from geometric stiffening and influenced by the effect of prestress at equilibrium. A tensegrity structure would therefore display nonlinear vibrations when excited in the direction of the infinitesimal flex, the "frequency" decreasing with amplitude. Movement in the direction of the flex occurs with only infinitesimal change in member length, and therefore under conventional models of material damping in members the motion would not vanish as rapidly as it would for a conventional oscillator. We study one particular tensegrity geometry for which we present the forcedisplacement relationship in analytical form and then examine the nonlinear vibrations. We observe the role of damping and we discuss those implications for the design of tensegrity structures in space applications.The dynamic behavior of a simple elastic tensegrity structure is examined, in order to validate observations that the natural damping of the elastic elements in such a structure is poorly mobilized, due to the natural flexibility of the equilibrium position of the structure. It is confirmed, analytically and numerically, that the energy decay of such a system is slower than that of a linearlydamped system. (C) 2001 Editions scientifiques et medicales Elsevier SAS.]A tensegrity structure is a special truss structure in a stable equilibrium with selected members designated for only tension loading, and the members in tension form a continuous network of cables separated by a set of compressive members. This paper develops an explicit analytical model of the nonlinear dynamics of a large class of tensegrity structures, constructed of rigid rods connected by a continuous network of elastic cables. The kinematics are described by positions and velocities of the ends of the rigid rods, hence, the use of angular velocities of each rod is avoided. The model yields an analytical expression for accelerations of ail rods, making the model efficient for simulation, since the update and inversion of a nonlinear mass matrix is not required. The model is intended for shape control and design of deployable structures. Indeed, the explicit analytical expressions are provided herein for the study of stable equilibria and controllability, but the control issues are not treated in this paper. (C) 2001 The Franklin Institute. Published by Elsevier Science Ltd. All rights reserved.Tensegrity structures consist of strings (in tension) and bars (in compression). Strings are strong, light, and foldable, so tensegrity structures have the potential to be light but strong and deployable. Pulleys, NiTi wire, or other actuators to selectively tighten some strings on a tensegrity structure can be used to control its shape. This article describes some principles we have found to be true in a detailed study of mathematical models of several tensegrity structures. We describe properties of these structures which hold quite generally. We describe how pretensing all strings of a tensegrity makes its shape robust to various loading forces. Another property asserts that the shape of a tensegrity structure can be changed substantially with little change in the potential energy of the structure. Thus shape control should be inexpensive. This is in contrast to the control of classical structures which require substantial energy to change their shape.tIn this paper we formulate the general prestressability conditions for tensegrity structures. These conditions are expressed as a set of nonlinear equations and inequalities on the tendon tensions. Several examples of tensegrity structures for which the prestressability conditions can be analytically solved are then presented. (C) 2001 Published by Elsevier Science Ltd.JNOVELTY  The base module is constructed from six rigid bars (1) connected at one end to a central node (2), while their outer ends (3) are connected by pretensioned cables (4) to form eight triangular faces of a polyhedron. The central node is made from two components, each with three of the bars attached to it by pivots; the two components are connected by a central bolt which enables all the cables to be prestressed. In variants of the design the number of bars can be greater than six, and the bars and cables can be of different lengths to form structures of different geometrical shapes from the modules. USE  Base module for spatial structure using principle of 'Tensegrity' (a contraction of Tension and Integrity coined by US inventor Buckminster Fuller). ADVANTAGE  The module has simpler geometry and is easier to assemble.In this contribution tubular structures are considered from the point of view of a designer, who combines architectural design with structural design and industrial design. In his practice design is combined with development and research and all preparation activities are combined with those of production and realisation on the building site. Morphology, being the science of form, plays its role everywhere in the design process. It is present in the initial stage, in the final design and in the engineering. But on the other hand both on the level of global form finding of the complete building as an artefact and on the level of the composing building parts it plays a role up to the composing components and elements, in the detailing and in fact also in the choice of materials. In the last decade a remarkable change in attitude towards morphology has taken place in the minds of some of the most avant garde architects. This usually concerns the overall building form. However, designing and developing form is just one of the many aspects in an integrated design process in which many aspects with mutual influences are involved. For an architect, morphology as an isolated item is not very interesting as in the design process it has to match many other considerations and usually will be compromised. Structural morphology is interesting in so far as it poses the opportunity of developing new types of structures from a morphological point of view. Tubular structures offer an excellent opportunity to create efficient structures as well structures with a high spatial impact. From the design and build praxis of the author a number of new types of recent structures following the 'tensegrity' principle and making use of stainless steel tensile rods and tubular steel and in some cases even tubular glass compression bars are presented for ultra slender roof and facade structures covered with transparent glass panels.Tensegrities are a special type of tensile structures that offer a viable alternative to conventional space covering structures. The morphology of tensegrity networks is uniquely and directly related to their structural and mechanical properties. Geometric and topological complexity is a characteristic of the morphology of tensegrity structures and accounts for significant difficulties in the study of their initial configuration, and possibly, for their limited application in building design. In this paper a computer visualization method that involves animation procedures is proposed as a tool for the exploration of their form. The method is based on a graphical approach to the solution of their complex 3D geometry that combines CAD tools with Descriptive Geometry procedures. The display of the tensegrity structure as an animation of moving Paris, allows designers to asses the effect of a given geometric parameter on their architectural form.jA procedure for the nonlinear elastoplastic analysis of tensegrity systems under static lends is presented. This procedure considers both geometric and material nonlinearities, using an updated Lagrangian formulation and a modified NewtonRaphson iterative scheme with incremental loading. The applicability of this procedure is demonstrated through the study of the elastoplastic behavior of a five module tensegrity beam. The effect of the yielding of some cable elements on the initial defined relational geometry once a tensegrity system is unloaded is outlined. (C) 2000 Elsevier Science Ltd. All rights reserved.qConsider a planar linkage, consisting of disjoint polygonal arc< s and cycles of rigid bars joined at incident endpoints (polygonal chains), with the property that no cycle surrounds another are or cycle. We prove that the linkage can be continuously moved so that the arcs become straight, the cycles become convex, and no bars cross while presenting the bar lengths. Furthermore, our motion is piecewisedifferentiable, does not decrease the distance between any pair of vertices, and preserves any symmetry present in the initial configuration. In particular this result settles the wellstudied carpenter's rule conjecture.A living organism represents the ultimate complex adaptive system. Our work focuses on the question of how groups of molecules selforganize to create living cells and tissues with emergent properties, such as the ability to change shape, move, and grow. Most complexitybased approaches focus on nodes, connections, and resultant pattern formation. We have extended this approach by taking into account the importance of architecture, mechanics and structure in the evolution of biological form. This work has led to the discovery of fundamental design principles that guide selfassembly in natural systems, from the simplest inorganic compounds to the most complex living cells and tissues. These building rules are based on the use of a particular form of geodesic architecture, known as tensegrity, which causes hierarchical collections of different interacting components to selforganize and mechanically stabilize in three dimensions. Shape and pattern stability emerge through establishment of a force balance between globally acting attractive (tensile) forces and locally acting repulsive (compressive) forces or, in simplest terms, through continuous tension and local compression (tensional integrity or "tensegrity"). Recent development of a mathematical explanation for the mechanical behavior of living cells and tissues based on tensegrity may provide a useful computational tool for analysis in other complex adaptive systems ranging from protein folding to cosmology.5Tensegrity structures are underconstrained, 3dimensional, selfstressing structural systems. They demonstrate an infinitesimal flex and when loaded they display a nonlinear geometric stiffening. In earlier work many examples of the resulting forcedisplacement relationship have been demonstrated numerically, and some aspects of the forcedisplacement relationship have been derived analytically. In this article an energy formulation is presented for the case of a simple but representative tensegrity structure, yielding an exact solution for the forcedisplacement relationship. The solution makes understandable the different appearance of the forcedisplacement relationship when comparing a system at zero prestress to one at high prestress, or when comparing a system with almostinextensible members to one with highly extensible members. The exact solution also is offered as a benchmark against which numerical solutions should be tested. Furthermore, the formulation and the solution reveal conditions of asymmetry of response that have not been noted previously.In this paper we propose a new motion simulator based on a tendoncontrolled tensegrity structure. The simulator is equipped with a nonlinear controller that achieves robust tracking of desired motions. The controller parameters can be tuned to guarantee tracking to within a prespecified tolerance and with a prescribed rate of exponential convergence. The design is verified through numerical simulations for specific longitudinal motions of a symmetric aircraft.Biology contains many examples of deployable structures. They can be grouped as planar, cylindrical, stiff and compliant, and space frame combining both stiff and compliant elements (tensegrity structures). Deployment occurs due to high strain elastic materials, or folds and curves that can be actuated by springs, changes in shape (mediated by hydraulic or contractile mechanisms) or changes in stiffness. Evolution filters out inefficiency. Transfer of nature's technology requires understanding of the optimizations in the biological system. The concepts can then be used in aerospace, deployable camouflage, packaging, emergency shelters, capture systems, etc.We have tried to understand the role of cellular tone (or internal tension mediated by actin filaments) and interactions with the microenvironment on cellular stiffness. For this purpose, we compared the apparent elasticity modulus of a 30element tensegrity structure with cytoskeleton stiffness measured in subconfluent and confluent adherent cells by magnetocytometry, assessing the effect of changing cellular tone by treatment with cytochalasin D. Intracellular and extracellular mechanical interactions were analyzed on the basis of the nondimensional relationships between the apparent elasticity modulus of the tensegrity structure normalized by Young's modulus of the elastic element versus: (i) element size; (ii) internal tension, and (iii) number of spatially fixed nodes, for small deformation conditions. Theoretical results and rigidity measurements in adherent cells consistently showed that higher cellular tone and stronger interdependencies with cellular environment tend to increase cytoskeleton stiffness. Visualization of the actin lattice before and after depolymerization by cytochalasin D tended to confirm the geometrical and mechanical assumptions supported by analysis of the present model.To describe the relationship between shape and rigidity of cultured cells, we attempt to figure out the similarities and discrepancies in geometrical and mechanical behaviors between a continuous cellular solid and a tensegrity structure. The rigidity of the structure is characterized by elementary bending in cellular solid and a spatial rearrangement of the elements in tensegrity model. This spatial reorganization tends to decrease the scale factor influence in tensegrity model. This factor has a major effect in cellular solid model in spite of the lack of internal tension. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.0The concept of tensegrity as conceived by Buckminster Fuller has been incorporated into a passive hydrophone device. Tensegrity is described as the physical phenomenon that produces a stable geometric structure using solid compressional elements arranged in tandem with Flexible tensional cables. In the devices built by the authors, six PZT 5H(TM) bars acting as compressional elements in the tensegrity structure have been coupled with tensional bands of either polyaramid or carbon fiber. This stable system is then wrapped with an outer layer of either polyaramid or carbon fiber and rubber film to form a sealed device, which is referred to as a piezotensegritive device in this paper. The six bars are arranged in parallel electrical connectivity for all devices described. The resonant frequency for these devices ranged from 19.5 to 20.3 kHz depending on the material used for wrapping the piezoelectric bars. These devices were also tested in a hydrostatic environment to determine the relevant piezoelectric coefficients. For devices wrapped with carbon fiber, d(h) peaked at similar to 6000 pC/N and g(h) at similar to 275 mVm/N. For devices wrapped with polyaramid, d(h) peaked at similar to 2000 pC/N and g(h) at similar to 100 mVm/N. Sensitivities from 182195 db ref. 1 V/mu Pa were calculated for these devices.With vast changes realized in the development of spacecraft systems over the last decade, it is clear that a cheaper approach is needed for kinematic systems such as parabolic antenna reflectors. Historically, these meshsurface reflectors have resembled folded umbrellas, with advances in multiple radial folds utilized to save packaging size. This work addresses a new kinematic approach to deployable antenna design utilizing tensegrity structures, which were invented by Kenneth Snelson, a student of R. Buckminster Fuller, in 1948. Such structures use a minimum number of struts and tension members, called ties, maintain stability. The novelty introduced here is that the ties are elastic. The authors have developed an approach < to quantify the stability of parallel manipulator designs that can be applied to deployable tensegrity antenna structures. Based on previous 33 (octahedron) and 44 (square antiprism) research, 66 (hexagonal antiprism) analysis has been completed that establishes usable parameters. The primary objective is to prove the stability of this class of deployable structures, and therefore their potential application to space structures. The secondary objective Is to define special motions for tensegrity antennas, which meet subsystem design requirements.Piezoelectricity and tensegrity have been coupled into an electrically active device. This concept, hereby known as piezotensegrity, can be used to sense or actuate. A composite sensor has been tested using compression elements stabilized with tensioning bands. The piezoelectric elements are arranged on the face diagonals with perimeter tension bands. Experimental piezoelectric response from this design was 1200 pC/N in air testing with peak hydrostatic response of 700 pC/N. The good device sensitivity as compared to properties of the base piezoelectric material is attributed to the internal arrangement of the piezoelectric elements and the tensioning system.The present paper reports a study on optimization for maximum stiffness of a fullscale cable dome, which has a 240 x 190 m elliptic plan and is roofed with membrane. The optimization performed in this study indicated that the optimum shape of the dome depends greatly on the length of the outermost posts. It was thus found that the vertical displacement in the area along the minor axis, which is usually big and difficult to reduce for an elliptic cable dome, can be reduced 25 similar to 35% by increasing 20% of the length of the outermost posts. The dependence of the optimality upon the design parameters were represented in terms of: (1) the slope of the descent path of the objective function during optimization iteration; (2) the slope of the surface of optima. Such a representation is very helpful for designers to evaluate the dependence of the optimality upon the design parameters so as to make design decisions accordingly. (C) 1999 Elsevier Science Ltd. All rights reserved.&A calculation method for structures with large deformations and displacements, based on works by Bathe [79], is developed so as to determine the tangent stiffness matrix and the internal stress vector. The formulation is established for a 'bar' element. Application of this method for tensegrity systems allowed the study of behaviour for a simple selfstressed system, the fourstrut tensegrity system, in case of 'traction, compression, flexion and torsion' loading. Except for compression, the structure is rigidified when the loads increase. Influence of the selfstress level on this behaviour is also evaluated. Secondly a structure, generated by assembly of several fourstrut tensegrity systems, has been calculated only under traction, concentrated and distributed. The behaviour under uniformly distributed load can be related to the 'isolate' cell behaviour, even if some difficulties appear, mainly because of boundary conditions. and possible choices for common cables between two adjacent cells. (C) 1999 Elsevier Science Ltd. All rights reserved.This paper considers the problem of minimizing a quadratic function on a Hilbert space subject to an affine constraint when the associated bilinear function is elliptic over the null space of the constraint operator. It develops a multiscale theory for constrained optimization and relates it to multiresolution analysis and wavelets thru several examples. It also suggests potential applications to study the mechanics of tensegrity structures and tethered membranes.The aim of this work was to study the morphological behavior and the surface adhesion molecules expression and localization of a human endothelial cell line subjected in vitro to a laminar flow in a parallel plate flow chamber, by a 3D fluorescence microscopy and cytofluorimetry. At rest, endothelial cells showed an array of microfilament bundles of the actin fibers, and a peripheral distribution of ICAM1 molecules. After shear stress (1 to 30 dyne/cm(2), 1 to 24 hours), the stress fibers appeared and were oriented related to the flow direction but also to the shear. The ICAM1 expression varied according to the shear stress characteristics and their distribution at the cell surface appeared also modified and related to the stress fibers formation.vTensegric system is an optimum structural form in which the behavior of high strength in steel cable can be utilized, but the reliability of this system is not very good because of the quasivariable characteristics. Cablenets are also an effective structure that could span large space. This paper proposes a new concept of spatial structure in which we combine tensegrity with cablenets to form a quasitensegric system. So we can make use of the advantages of these two systems. A construction manner is developed. A quasitensegric system could be formed by the tensegric elements. This paper divides the equilibrium state of quasitensegric system into two states: one is geometrical stable equilibrium state, the other is elastic state equilibrium state. A method is developed to calculate the form and internal forces in the geometrical stable equilibrium state and the convergence is provided. The results of calculating show that the method proposed has a good convergence and a high precision. Comparing incremental iterative method with dynamic relaxation method, the two methods are effective and reliable in engineering design.Tensegrity systems have been known for almost half a century. Their mechanical and geometrical characteristics make them suitable to terrestrial and extraterrestrial applications. This paper describes a numerical scheme of active control of tensegrity systems in extraterrestrial applications. An algorithm based on instantaneous optimal control has been developed and applied to an assembly of elementary tensegrity cells. The whole structural system comprises four cells forming a linear structure with 27 cables and 12 struts. Active control is realized in the first simulation by means of three actuators and in the second by means of six actuators located on two of the four cells. The results show that vibration amplitudes of nodes are reduced by such an active control scheme.Bolker and Crape gave a graph theoretical model of square grid frameworks with diagonal rods of certain squares. Baglivo and Graver solved the problem of tensegrity frameworks where diagonal cables may be used in the square grid to make it rigid. The problem of onestory buildings in both cases can be reduced to the planar problems. These results are generalized if some longer rods, respectively some longer cables are also permitted.Tin this study, a dynamic analysis of the selfstress level of tensegrity systems is established A direct relation Between the natural frequencies of these systems and the selfstress level of their cable components was established If constitutes a first step toward the study of the adaptability of tensegrity systems to external loads. The adaptability would result of different procedures, By regulation of the selfstress of one or several cable elements. The threestruts tensegrity system was used. The frequencies and mode shapes were determined for a defined selfstress level. The evolution of the natural frequencies with the selfstress level of a reference cable component were computed for one module and for an assembly of 2,3,4 and 5 modules. The plot of this evolution can serve as an abacus that can Be used to find the selfsfress level corresponding to a required frequency of the system and vice versa.The concept of cablestrut is extended from that of tensegrity. The broad interpretation of cablestrut systems includes tensegrity systems, RP (Reciprocal Prism) and CP (Crystalcell Pyramid) system, etc. Its narrow interpretation excludes tensegrity systems. Thus this paper is divided into two parts. Part I gives concept, properties and feasibility studies of tensegrity structures to put forward cables< trut systems. Part II presents the theory and novel concepts concerning the application of cablestrut systems, and concludes that cablestrut systems are revolutionary in space structures. In this part, the essential idea of tensegrity is analyzed and the concept of tensegrity is systematically redefined. Tensegrity grids can be classified into Two types of configurations: noncontiguous strut and contiguous strut. Their properties are presented and compared. The properties of the latter are also compared with those of RP grids. The low efficiency of tensegrity grids is analyzed. The feasibility studies, concerning applicable tensegrity forms and their application scale, are also introduced in this paper. (C) 1998 Elsevier Science Ltd. All rights reserved.aIn this part, the basic concept of cablestrut systems is introduced. Cablestrut systems, including reciprocal prism (RP) and cell pyramidal (CP) grids invented by the author, as successful attempts to introduce cables into simplexes to form grids, are revolutions in space structures. Their properties are presented in this paper. Cablestrut systems possess selfstressed equilibrium, avoiding reliance on a bulky anchorage system, which is a most important advantage in construction over conventional flexible structures. It has improved greatly the structural properties of tensegrity systems, which also possess selfstressed equilibrium. Its planar form becomes the lightest selfstressed equilibrium space bar systems. The additional advantages over conventional space bar systems are that its joint design can be simplified, and its grid depth and grid length cart be adjusted easily to sustain large bar forces and to lower bar forces further. Moreover, its stiffness can be increased by introducing bars to replace connecting cables to form doublelayer and triplelayer forms. Superspan domical and cylindrical forms of RP system have also proved to be feasible and economical. The advantage of cablestrut systems in architecture is that the systems are clear in sense of sight, which makes them very attractive. (C) 1998 Elsevier Science Ltd All rights reserved._The Tensegrity model has a series of rods strung into a mathematical shape by support threads. To provide support, the threads are threaded through slots in the ends of the rods and retained by knots.The knots can be inside or outside the rods. No other fasteners are required.ADVANTAGE  Secure structure without having to balance tension in threads.There is a growing demand for new and renovated stadia and an increasing market opportunity for the concrete industry. This paper traces the history of the modern stadia and explores the growing use of concrete.A tensegrity structure composed of six slender struts interconnected with 24 linearly elastic cables is used as a model of cell deformability. Struts are allowed to buckle under compression and their postbuckling behavior is determined from an energy formulation of the classical pinended Euler column. At the reference state, the cables carry initial tension balanced by forces exerted by struts. The structure is stretched uniaxially and the stretching force versus axial extension relationships are obtained for different initial cable tensions by considering equilibrium at the joints. Structural stiffness is calculated as the ratio of stretching force to axial extension. Predicted dependences of structural stiffness on initial cable tension and on stretching force are consistent with behaviors observed in living cells. These predictions are both qualitatively and quantitatively superior to those obtained previously from the model in which the struts are viewed as rigid.EThe National Hockey League's Buffalo Sabres have a new home, topped with an unusual tensionbraced domed roof. An ingenious combination of dome designs, the Marine Midland Arena's roof combines the lightweight, clearspan advantage of a tensegrity cable dome with the clean and simple load path of a singlelayer braced dome.The structure includes tensegrity module (1O) with several tension materials (12,13) which surround pair of crossing compression materials. The compression materials withstand the compression power of rod for instance as the tension materials withstand the pulling power of wire for instance.The compression materials of adjustable length meander along the stretch direction of the tension materials.ADVANTAGE  Offers structure with improved degree of designing.This paper defines two concepts of rigidity for tensegrity frameworks (frameworks with cables, bars, and struts): prestress stability and secondorder rigidity. We demonstrate a hierarchy of rigidityfirstorder rigidity implies prestress stability implies secondorder rigidity implies rigidityfor any framework. Examples show that none of these implications are reversible, even for bar frameworks. Other examples illustrate how these results can be used to create rigid tensegrity frameworks. This paper also develops a duality for secondorder rigidity, leading to a test which combines information on the self stresses and the firstorder flexes of a framework to detect secondorder rigidity. Using this test, the following conjecture of Roth is proven: a plane tensegrity framework, in which the vertices and bars form a strictly convex polygon with additional cables across the interior, is rigid if and only if it is firstorder rigid.+This is the second part of a twopart paper on the general review of static, dynamic, and thermal analysis methods, and special topics for the design of doublelayer grids (DLG). This work forms part of the anticipated report. of the ASCE Task Committee on Double Layer Grids. In this paper the current stateoftheart information pertaining to the dynamic analysis techniques and special topics for the DLG structural system are reviewed with references to both practical and research tools for analysis. A comprehensive reference list is provided, which covers many conventional and emerging topics related to the analysis of DLGs. Topics presented include dynamic linear, nonlinear and stability analyses, dynamic loadings, progressive collapse, dynamic effects of member failure, optimization techniques, probabilistic methods, vibration control, system identification and damage detection, special application DLGs, and other newly emerging analysis methods. The first paper dealt with static and thermal analysis and member behavior. The information presented in this paper is useful to the practicing engineer and for research. Some of the information though not directly applicable in routine design, may have to be considered for special cases and as the design and construction capabilities of DLGs are enhanced.The module (10) consists of an upper surface (A) and a lower surface (B). A central north pole (N0) is formed on the centre of the upper surface. Similarly three peripheral north poles (N1,N2,N3) are formed on the corners of the upper surface. Similarly, a central south pole (S0) and three peripheral south poles (S1S3) are formed on the lower surface. A number of pillar shaped members (1) are provided to couple the central force with the peripheral poles on each surface.A first wire rod (2a) is provided to couple the peripheral poles together. A second wire rod (2b) is provided to couple the peripheral poles of each surface. Similarly a third wire rod (2c) couples the central pole of supper surface with the central pole of the lower surface and the peripheral poles of upper surface with the peripheral poles of the lower surface individually.ADVANTAGE  Provides independent structure. Reduces tilt work. Makes transportation and storage easy.We give a characterization of the planar layouts of configurations with at most five lines. From this we obtain a new proof of Viro's theorem that the isotopy type of such configurations is completely determined by chirality. We extend this result to labelled configurations. We also give an infinite family of nonrealizable line diagrams, called 'alternating Cangles', not containing nonrealizable subdiagrams.The structure has roof structure incorporating stressed cables (4) and comp<Uressed struts (8,9).The structure is supported by lugs (6) and is such that it can be readily erected by tensioning the cables after positioning the lugs.The cables may be attached to a hinged collapsible floor (14) so that when the floor is extended into its final shape,the cables are automatically tensioned.Walls may be formed by spaced skins (18) of e.g. plywood, with insulating material positioned in sachets (20) between the skins.ADVANTAGE  By employing the principle of tensegrity to support the roof, the interior of the structure is not unnecessarily cluttered by the provision of internal supports for the roof and the area spanned by the roof has no inherent size limitations.The minimum number of diagonal cables to make a onestory building infinitesimally rigid and the characterization of the minimum systems in two special cases were given in Part I and Part II. We now characterize the minimum systems in the general case.zSome recent results are presented, concerning the algorithmic aspects of 2dimensional generic rigidity, and 1story buildings as tensegrity frameworks. Most of these results were obtained after the completion of the first survey (Recski, 1984) for a 'Winter School' organized by the late Professor Z. Frolik. Results in Sections 3 and 4 of the first survey are used throughout.This paper discusses the analytical conditions under which a pinjointed assembly. which has s independent states of selfstress and m independent mechanisms. tightens up when its mechanisms are excited. A matrix algorithm is set up to distinguish between firstorder infinitesimal mechanisms (which are associated with secondorder changes of bar length) and higherorder infinitesimal or finite mechanisms. It is shown that. in general. this analysis requires the computation of. v quadratic forms in m variables. which can be easily computed from the states of selfstress and mechanisms of the assembly. If any linear combination of these quadratic forms is sign definite. then the mechanisms are firstorder infinitesimal. An efficient and general algorithm to investigate these quadratic forms is given. The calculations required are illustrated for some simple examples. Many assemblies of practical relevance admit a single state of selfstress (s= 1), and in this case the algorithm proposed is straightforward to implement. This work is relevant to the analysis and design of prestressed mechanisms. such as cable systems and tensegrity frameworks._Tensegrity structures are freestanding prestressed cable networks in which the cables are prestressed against a discontinuous system of bars. In doublelayer tensegrity grids (DLTGs), the bars are confined between two parallel layers of cables. This paper presents the analytical part of an investigation of a type of DLTG. A firstorder linear analytical model indicates that these structures possess low stiffness and low bar force efficiency. Under full prrestress, determined by the condition that no cable is slack under the applied load, the model predicts deflections of approximately 1/20 of the span, and 20% of bar loadbearing capacity is available for the applied load, the rest being required by prestress. Member forces and deflections are strongly affected by the span, structural depth and level of prestress. Enhancement techniques are discussed.Tensegrity structures are freestanding prestressed cable networks in which the cables are prestressed against a discontinuous system of bars. In doublelayer tensegrity grids (DLTGs), the bars are confined between two parallel layers of cables. This is the second paper in a twopart analytical and experimental study of a type of DLTG. The first part, presenting results of a firstorder linear analytical model, indicates that these structures posses low stiffness and low bar force efficiency. The experimental investigation of a smallscale model indicates that actual response is significantly nonlinear and that both stiffness and bar force efficiency are higher than indicated by the linear model. Member forces due to the applied load are generally higher than the linear model indicates. A nonlinear analytical model is generally in good agreement with the results. The concept, consisting of independent prismatic units, possesses a high degree of structural redundancy. Loadbearing capacity is practically unaffected by the loss of a member.YThe building is designed according to a precise mathematical formula from which all points of juncture for struts or plates may be readily determined. The formula is a variant of the helix formula and when it is applied in both a clockwise and counterclockwise manner to the surface of a sphere, ellipse, or such like shape, it definese a polygonal grid on the surface. The counterclockwise spirals from base to zenith are eccentric in that they do not proceed from base to zenith in the same number of degrees as the clockwise spirals.As a result of the eccentricity of the spirals, an eccentric pattern of polygons emerges whereby connections of apices across the polygons do not yield symmetric triangles. When connections are made across the polygons in both directions, horizontal and diagonal, the resultant pattern becomes geodesic and gains additional strength from the engineering principle of tensegrity which results.USE/ADVANTAGE  Conventional shaped and sized apertures may be provided for doors or windows, or for panels allowing one or more structures to be easily conjoined. @(24pp Dwg.No.1/28)@A tensegrity structure is formed from interconnected tensegrity modules. Each module includes several columnlike compression members. Tension elements run between ends of the compression members to define a polyhedron. The tension elements form the edges of the polyhedron and intersect at the vertices of the polyhedron.The interconnected modules are joined to each other with triangular faces abutting but with the edges and faces of the abutting triangular surfaces of the respective modules rotated 180 deg. away from superposition and with the vertices joined to tension element edges. Further, they are joined at a point located onehalf or onethird of the way along the length of the edge.12b46z78I[:<y
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