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Research Papers

Kinematic, Stiffness, and Dynamic Analyses of a Compliant Tensegrity Mechanism

[+] Author and Article Information
Bahman Nouri Rahmat Abadi

School of Mechanical Engineering,
Shiraz University,
Shiraz 71348-51154, Iran
e-mail: bahmannouri1@gmail.com

S. M. Mehdi Shekarforoush

School of Mechanical Engineering,
Shiraz University,
Shiraz 71348-51154, Iran
e-mail: mshekarforoush@yahoo.com

Mojtaba Mahzoon

School of Mechanical Engineering,
Shiraz University,
Shiraz 71348-51154, Iran
e-mail: mahzoon@shirazu.ac.ir

Mehrdad Farid

School of Mechanical Engineering,
Shiraz University,
Shiraz 71348-51154, Iran
e-mail: farid@shirazu.ac.ir

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received March 11, 2012; final manuscript received May 2, 2014; published online June 5, 2014. Assoc. Editor: Andrew P. Murray.

J. Mechanisms Robotics 6(4), 041001 (Jun 05, 2014) (8 pages) Paper No: JMR-12-1027; doi: 10.1115/1.4027699 History: Received March 11, 2012; Revised May 02, 2014

The objective of this study is to present an analytical procedure for analysis of a compliant tensegrity mechanism focusing on its stiffness and dynamic characteristics. The screw calculus is used to derive the static equations and stiffness matrix of a full degree-of-freedom tensegrity mechanism, and the equations of motion are derived based on the principle of virtual work. Finally, some numerical examples are solved for the inverse dynamics of the mechanism.

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References

Fuller, R. B., 1962, “Tensile-Integrity Structures,” U.S. Patent No. 3,063,521.
Pugh, A., 1976, An Introduction to Tensegrity, University of California Press, Berkeley, CA.
Motro, R., 2011, “Structural Morphology of Tensegrity Systems,” Meccanica, 46(1), pp. 27–40. [CrossRef]
Hanaor, A., 1994, “Geometrically Rigid Double-Layer Tensegrity Grids,” Int. J. Space Struct., 9(4), pp. 227–238.
Bayat, J., and Crane, C. D., III, 2007, “Closed-Form Equilibrium Analysis of Planar Tensegrity Structures,” 31st Mechanisms and Robotics Conference, Parts A and B, Las Vegas, NV, Vol. 8, pp. 13–23.
Arsenault, M., and Gosselin, C., 2006, “Kinematic, Static and Dynamic Analysis of a Planar 2-DoF Tensegrity Mechanism,” Mech. Mach. Theory, 41(9), pp. 1072–1089. [CrossRef]
Chen, S., and Arsenault, M., 2012, “Analytical Computation of the Actuator and Cartesian Workspace Boundaries for a Planar 2-Degree-of-Freedom Translational Tensegrity Mechanism,” ASME J. Mech. Rob., 4(1), p. 011010. [CrossRef]
Crane, C. D., Correa, J. C., and Duffy, J., 2005, “Static Analysis of Tensegrity Structures,” ASME J. Mech. Des., 127(2), pp. 257–268. [CrossRef]
Arsenault, M., and Gosselin, C., 2006, “Kinematic, Static, and Dynamic Analysis of a Spatial Three-Degree-of-Freedom Tensegrity Mechanism,” ASME J. Mech. Des., 128, pp. 1061–1069. [CrossRef]
Arsenault, M., and Gosselin, C., 2008, “Kinematic and Static Analysis of 3-PUPS Spatial Tensegrity Mechanism,” Mech. Mach. Theory, 44, pp. 162–179. [CrossRef]
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Shekarforoush, S. M. M., Eghtesad, M., and Farid, M., 2013, “Kinematic and Static Analyses of Statically Balanced Spatial Tensegrity Mechanism With Active Compliant Components,” J. Intell. Robot. Syst., 71(3–4), pp. 287–302. [CrossRef]
Nouri Rahmat Abadi, B., Farid, M., and Mahzoon, M., 2014, “Introducing and Analyzing a Novel Three-Degree-of-Freedom Spatial Tensegrity Mechanism,” J. Comput. Nonlinear Dyn., 9(2), p. 021017. [CrossRef]
Burkhardt, R. W., 2007, A Practical Guide to Tensegrity Design, 2nd ed., http://www.trip.net/~bobwb/ts/tenseg/book/cover.html
Knight, B., Zhang, Y., Duffy, J., and Crane, C., 2000, “On the Line Geometry of a Class of Tensegrity Structures,” Proceedings of Sir Robert Stawell Ball Symposium, University of Cambridge, UK.
Marshall, M. Q., 2003, “Analysis of Tensegrity-Based Parallel Platform Devices,” M.S. thesis, Center for Intelligent Machine and Robotics, Department of Mechanical and Aerospace Engineering, University of Florida, FL.
Zhang, D., 2010, Parallel Robotic Machine Tools, Springer, New York.
Sultan, C., and Skelton, R., 2004, “A Force and Torque Tensegrity Sensor,” Sens. Actuators, A, 112(2–3), pp. 220–231. [CrossRef]
Ball, R. S., 1900, A Treatise on the Theory of Screws, Cambridge University Press, New York.
Baruh, H., 1999, Analytical Dynamics, McGraw-Hill, International Edition, Singapore.
Shabana, A. A., 2001, Computational Dynamics, John Wiley & Sons, Inc., New York.

Figures

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Fig. 1

A CAD model of 3-3 Stewart platform

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Fig. 2

A CAD model of the presented tensegrity mechanism

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Fig. 3

A graphical plan of the proposed tensegrity mechanism

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Fig. 4

Schematic representation of a typical piston drive and tendon drive limb

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Fig. 5

Actuating forces versus time

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Fig. 6

The variation of lengths of the cables and pistons in the limbs

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Fig. 7

Actuating forces versus time

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Fig. 8

The variation of lengths of the cables and pistons in the limbs

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