Kinematic, Static, and Dynamic Analysis of a Spatial Three-Degree-of-Freedom Tensegrity Mechanism

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 one-degree-of-freedom tensegrity mechanism. This mechanism is obtained from a three-degree-of-freedom 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.

[1]  H. Schek.  The force density method for form finding and computation of general networks , 1974 .

[2]  Anthony Pugh,et al.  An Introduction to Tensegrity , 1976 .

[3]  Sergio Pellegrino,et al.  Mechanics of kinematically indeterminate structures , 1986 .

[4]  S. Pellegrino.  Analysis of prestressed mechanisms , 1990 .

[5]  S. Pellegrino,et al.  First-order infinitesimal mechanisms , 1991 .

[6]  Hiroshi Furuya,et al.  Concept of Deployable Tensegrity Structures in Space Application , 1992 .

[7]  René Motro,et al.  Tensegrity Systems: The State of the Art , 1992 .

[8]  S. Pellegrino.  Structural computations with the singular value decomposition of the equilibrium matrix , 1993 .

[9]  Robert Connelly,et al.  Second-Order Rigidity and Prestress Stability for Tensegrity Frameworks , 1996, SIAM J. Discret. Math..

[10]  Cornel Sultan,et al.  Controllable tensegrity: a new class of smart structures , 1997, Smart Structures.

[11]  Robert E. Skelton,et al.  Tendon control deployment of tensegrity structures , 1998, Smart Structures.

[12]  M. N. Kazi-Aoual,et al.  Geometrical non-linear analysis of tensegrity systems , 1999 .

[13]  René Motro,et al.  Multiparametered Formfinding Method: Application to Tensegrity Systems , 1999 .

[14]  Clément Gosselin.  Static Balancing of Spherical 3-DOF Parallel Mechanisms and Manipulators , 1999, Int. J. Robotics Res..

[15]  C. Sultan.  Modeling, design, and control of tensegrity structures with applications , 1999 .

[16]  Martin Corless,et al.  Peak-to-peak control of an adaptive tensegrity space telescope , 1999, Smart Structures.

[17]  Cornel Sultan,et al.  REDUCED PRESTRESSABILITY CONDITIONS FOR TENSEGRITY STRUCTURES , 1999 .

[18]  Irving J. Oppenheim,et al.  Geometric Effects in an Elastic Tensegrity Structure , 2000 .

[19]  Carl D. Crane,et al.  A review of a family of self-deploying tensegrity structures with elastic ties , 2000 .

[20]  Martin Corless,et al.  Tensegrity Flight Simulator , 2000 .

[21]  Irving J. Oppenheim,et al.  Vibration and Damping in Three-Bar Tensegrity Structure , 2001 .

[22]  I. Oppenheim,et al.  Vibration of an elastic tensegrity structure , 2001 .

[23]  Robert E. Skelton,et al.  An introduction to the mechanics of tensegrity structures , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[24]  Julio C. Correa,et al.  Static Analysis of Prestressed Tensegrity Structures , 2002 .

[25]  Tung Minh Tran.  REVERSE DISPLACEMENT ANALYSIS FOR TENSEGRITY STRUCTURES , 2002 .

[26]  M. Corless,et al.  Linear dynamics of tensegrity structures , 2002 .

[27]  Joseph Duffy,et al.  Static Analysis of Tensegrity Structures: Part 1 — Equilibrium Equations , 2002 .

[28]  Joseph Duffy,et al.  Static Analysis of Tensegrity Structures: Part 2 — Numerical Examples , 2002 .

[29]  Gunnar Tibert,et al.  Deployable Tensegrity Structures for Space Applications , 2002 .

[30]  Gunnar Tibert,et al.  Deployable tensegrity masts , 2003 .

[31]  A. Tibert,et al.  Review of Form-Finding Methods for Tensegrity Structures , 2003 .

[32]  Cornel Sultan,et al.  A force and torque tensegrity sensor , 2004 .

[33]  Carl D. Crane,et al.  Design and Analysis of a Hybrid Parallel Platform That Incorporates Tensegrity , 2004 .

[34]  Thomas Gerstner,et al.  Numerical integration using sparse grids , 2004, Numerical Algorithms.

[35]  Julio C. Correa,et al.  Static Analysis of Tensegrity Structures , 2005 .

[36]  Clément Gosselin,et al.  Static Balancing of Tensegrity Mechanisms , 2005 .

[37]  Clément Gosselin,et al.  Kinematic, static and dynamic analysis of a planar 2-DOF tensegrity mechanism , 2006 .

[38]  Carl D. Crane,et al.  Closed-Form Equilibrium Analysis of Planar Tensegrity Structures , 2007 .