One 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 three-degree-of-freedom 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.
Issue Section:
Research Papers
1.
Fuller
, B.
, 1975, Synergetics: The Geometry of Thinking
, MacMillan
, New York.2.
Motro
, R.
, 1992, “Tensegrity Systems: The State of the Art
,” Int. J. Space Struct.
0956-0599, 7
, pp. 75
–83
.3.
Pugh
, A.
, 1976, An Introduction to Tensegrity
, 1st ed., University of California Press
, Los Angeles, CA.4.
Duffy
, J.
, Rooney
, J.
, Knight
, B.
, and Crane
, C. D.
, III, 2000, “Review of a Family of Self-Deploying Tensegrity Structures with Elastic Ties
,” Shock Vib. Dig.
0583-1024, 32
, pp. 100
–106
.5.
Sultan
, C.
, and Skelton
, R. E.
, 1998, “Tendon Control Deployment of Tensegrity Structures
,” in Proceedings of SPIE - The International Society for Optical Engineering
, Vol. 3323
, pp. 455
–466
.6.
Tibert
, G.
, 2002, “Deployable Tensegrity Structures for Space Applications
,” Ph.D. thesis, Department of Mechanics, Royal Institute of Technology, Stockholm, Sweden.7.
Furuya
, H.
, 1992, “Concept of Deployable Tensegrity Structures in Space Application
,” Int. J. Space Struct.
0956-0599, 7
, pp. 143
–152
.8.
Calladine
, C. R.
, and Pellegrino
, S.
, 1991, “First-Order Infinitesimal Mechanisms
,” Int. J. Solids Struct.
0020-7683, 27
, pp. 505
–515
.9.
Pellegrino
, S.
, 1993, “Structural Computations with the Singular Value Decomposition of the Equilibrium Matrix
,” Int. J. Solids Struct.
0020-7683, 30
, pp. 3025
–3035
.10.
Pellegrino
, S.
, 1990, “Analysis of Prestressed Mechanisms
,” Int. J. Solids Struct.
0020-7683, 26
, pp. 1329
–1350
.11.
Vassart
, N.
, and Motro
, R.
, 1999, “Multiparametered Formfinding Method: Application to Tensegrity Systems
,” Int. J. Space Struct.
0956-0599, 14
, pp. 147
–154
.12.
Schek
, H.-J.
, 1974, “The Force Density Method for Form Finding and Computation of General Networks
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 3
, pp. 115
–134
.13.
Pellegrino
, S.
, 1986, “Mechanics of Kinematically Indeterminate Structures
,” Ph.D. thesis, University of Cambridge, United Kingdom.14.
Motro
, R.
, 1984, “Forms and Forces in Tensegrity Systems
,” in Proceedings of the 3rd International Conference on Space Structures
, pp. 180
–185
.15.
Tibert
, A. G.
, and Pellegrino
, S.
, 2003, “Review of Form-Finding Methods for Tensegrity Structures
,” Int. J. Space Struct.
0956-0599, 18
, pp. 209
–223
.16.
Sultan
, C.
, Corless
, M.
, and Skelton
, R. E.
, 1999, “Reduced Prestressability Conditions for Tensegrity Structures
,” in Proceedings of 40th AIAA/ASME/ASCE/AHS/ASC Structures
, Structural Dynamics and Materials Conference.17.
Kebiche
, K.
, Kazi-Aoual
, M.
, and Motro
, R.
, 1999, “Geometrical Non-Linear Analysis of Tensegrity Systems
,” Eng. Struct.
0141-0296, 21
, pp. 864
–876
.18.
Crane
, C. D.
, III, Duffy
, J.
, and Correa
, J. C.
, 2005, “Static Analysis of Prestressed Tensegrity Structures
,” ASME J. Mech. Des.
1050-0472, 127
, pp. 257
–268
.19.
Skelton
, R. E.
, Adhikari
, R.
, Pinaud
, J.-P.
, Chan
, W.
, and Helton
, J. W.
, 2001, “An Introduction to the Mechanics of Tensegrity Structures
,” in Proceedings of the IEEE Conference on Decision and Control
, Vol. 5
, pp. 4254
–4259
.20.
Oppenheim
, I. J.
, and Williams
, W. O.
, 2000, “Geometric Effects in an Elastic Tensegrity Structure
,” J. Elast.
0374-3535, 59
, pp. 51
–65
.21.
Sultan
, C.
, 1999, “Modeling, Design and Control of Tensegrity Structures With Applications
,” Ph.D. thesis, Purdue University.22.
Sultan
, C.
, Corless
, M.
, and Skelton
, R. E.
, 2002, “Linear Dynamics of Tensegrity Structures
,” Eng. Struct.
0141-0296, 24
, pp. 671
–685
.23.
Oppenheim
, I. J.
, and Williams
, W. O.
, 2001, “Vibration of an Elastic Tensegrity Structure
,” Eur. J. Mech. A/Solids
0997-7538, 20
, pp. 1023
–1031
.24.
Oppenheim
, I. J.
, and Williams
, W. O.
, 2001, “Vibration and Damping in a Three-Bar Tensegrity Structure
,” J. Aerosp. Eng.
0893-1321, 14
, pp. 85
–91
.25.
Tran
, T. M.
, 2002, “Reverse Displacement Analysis for Tensegrity Structures
,” Master’s thesis, University of Florida, Florida.26.
Oppenheim
, I. J.
, and Williams
, W. O.
, 1997, “Tensegrity Prisms as Adaptive Structures
,” ASME Adaptive Structures and Material Systems
, 54
, pp. 113
–120
.27.
Skelton
, R. E.
, and Sultan
, C.
, 1997, “Controllable Tensegrity, a New Class of Smart Structures
,” in Proceedings of SPIE—The International Society for Optical Engineering
, Vol. 3039
, pp. 166
–177
.28.
Arsenault
, M.
, and Gosselin
, C. M.
, 2005, “Kinematic, Static and Dynamic Analysis of a Planar 1-DoF Tensegrity Mechanism
,” ASME J. Mech. Des.
1050-0472, 127
, pp. 1152
–1160
.29.
Arsenault
, M.
, and Gosselin
, C. M.
, 2005, “Kinematic, Static and Dynamic Analysis of a Planar 2-DoF Tensegrity Mechanism
,” Mech. Mach. Theory
0094-114X, 41
(9
), pp. 1071
–1089
.30.
Bayat
, J.
, and Crane
, C. D.
, III, 2004, “Closed-Form Equilibrium Analysis of a Planar Tensegrity Structure
,” in Proceedings of the 9th International Symposium on Advances in Robot Kinematics
.31.
Marshall
, M.
, and Crane
, C. D.
, III, 2004, “Design and Analysis of a Hybrid Parallel Platform that Incorporates Tensegrity
,” in Proceedings of the ASME 2004 Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, pp. 535
–540
.32.
Sultan
, C.
, and Corless
, M.
, 2000, “Tensegrity Flight Simulator
,” J. Guid. Control Dyn.
0731-5090, 23
, pp. 1055
–1064
.33.
Sultan
, C.
, Corless
, M.
, and Skelton
, R. E.
, 1999, “Peak to Peak Control of an Adaptive Tensegrity Space Telescope
,” in Proceedings of SPIE - The International Society for Optical Engineering
, Vol. 3667
, pp. 190
–201
.34.
Sultan
, C.
, and Skelton
, R. E.
, 2004, “A Force and Torque Tensegrity Sensor
,” Sens. Actuators, A
0924-4247, 112
, pp. 220
–231
.35.
Snelson
, K.
, 1965, “Continuous Tension, Discontinuous Compression Structures
,” United States Patent No. 3,169,611, February 16.36.
Fuller
, B.
, “Tensile-Integrity Structures
, United States Patent No. 3,063,521, November 13, 1962.37.
Knight
, B.
, Zhang
, Y.
, Duffy
, J.
, and Crane
, C. D.
, III, 2000, “On the Line Geometry of a Class of Tensegrity Structures
,” in Proceedings of a Symposium Commemorating the Legacy, Works, and Life of Sir Robert Stawell Ball
.38.
Gosselin
, C. M.
, 1999, “Static Balancing of Spherical 3-DoF Parallel Mechanisms and Manipulators
,” Int. J. Robot. Res.
0278-3649, 18
, pp. 819
–829
.39.
Connelly
, R.
, and Whiteley
, W.
, 1996, “Second-Order Rigidity and Prestress Stability for Tensegrity Frameworks
,” SIAM J. Discrete Math.
0895-4801, 9
, pp. 453
–491
.40.
Arsenault
, M.
, and Gosselin
, C. M.
, 2005, “Static Balancing of Tensegrity Mechanisms
,” in Proceedings of the 2005 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE)
.Copyright © 2006
by American Society of Mechanical Engineers
You do not currently have access to this content.
