Compared with conventional mechanisms, tensegrity mechanisms have many attractive characteristics such as light weight, high ratio of strength to weight, and accuracy of modeling. In this paper, the kinematics, singularity, and workspaces of a planar 4-bar tensegrity mechanism have been investigated. Firstly, the analytical solutions to the forward and inverse kinematic problems are found by using an energy based method. Secondly, the definition of a tensegrity mechanism’s Jacobian is introduced. As a consequence, the singularity analysis of the planar 4-bar tensegrity mechanism has been completed. Thirdly, the actuator and output workspaces are mapped. Finally, some attractive characteristics of the mechanism are concluded. 1. Introduction As the complexity of robotic applications in space increases, new demands for lighter and quicker mechanisms arise. Tensegrity mechanisms can be viewed as one alternative solution to conventional mechanisms. For this reason, a planar 4-bar tensegrity mechanism is proposed in this paper and the kinematics and statics of the mechanism are studied. The term tensegrity was created by Fuller [1] as a combination of the words tensional and integrity. It seems that he was inspired by some novel sculptures completed by Snelson [2]. The detailed history of tensegrity systems was reviewed by Motro [3]. Tensegrity systems are formed by a set of compressive components and tensile components. Tensegrity systems have advantages of light weight, deployability, being easily tunable, and so forth. Due to these attractive characteristics, tensegrity systems have been used in several disciplines such as architecture, biology, aerospace, mechanics, and robotics during the last fifty years [4]. The applications of tensegrity systems can be divided into two main branches. One application is used as structures and the other one is used as mechanisms. In addition, the research of tensegrity structures has two main issues, which are the form-finding problem and the behaviors under external loads. The form finding of a tensegrity structure corresponds to the computation of the structure’s equilibrium shape for a given set of parameters. This problem has been studied by many authors [5–7]. Moreover, a review of form-finding methods is given by Tibert and Pellegrino [5]. The behaviors of tensegrity structures under external loads have also been researched by many researchers [8, 9]. A static analysis of tensegrity structures was given by Juan and Mirats Tur [10]. When some components (rigid rods or springs) are actuated, tensegrity mechanisms
References
[1]
B. Fuller, “Tensile-integrity Structures,” USA Patent 30,635,21, November 1965.
[2]
K. Snelson, “Continuous Tension, Discontinuous Compression Structures,” USA Patent 31,696,11, February 1965.
[3]
R. Motro, “Tensegrity systems: the state of the art,” International Journal of Space Structures, vol. 7, pp. 75–83, 1992.
[4]
R. E. Skelton and M. C. Oliveira, Tensegrity Systems, Springer, New York, NY, USA, 2009.
[5]
A. G. Tibert and S. Pellegrino, “Review of form-finding methods for tensegrity structures,” International Journal of Space Structures, vol. 18, no. 4, pp. 209–223, 2003.
[6]
K. Koohestani, “Form-finding of tensegrity structures via genetic algorithm,” International Journal of Solids and Structures, vol. 49, no. 5, pp. 739–747, 2012.
[7]
H. C. Tran and J. Lee, “Form-finding of tensegrity structures using double singular value decomposition,” Engineering with Computers, vol. 29, pp. 71–86, 2013.
[8]
N. Ben Kahla and K. Kebiche, “Nonlinear elastoplastic analysis of tensegrity systems,” Engineering Structures, vol. 22, no. 11, pp. 1552–1566, 2000.
[9]
A. Nuhoglu and K. A. Korkmaz, “A practical approach for nonlinear analysis of tensegrity systems,” Engineering with Computers, vol. 27, no. 4, pp. 337–345, 2011.
[10]
S. H. Juan and J. M. Mirats Tur, “Tensegrity frameworks: static analysis review,” Mechanism and Machine Theory, vol. 43, no. 7, pp. 859–881, 2008.
[11]
I. J. Oppenheim and W. O. Williams, “Tensegrity prisms as adaptive structures,” in in Proceedings of the ASME International Mechanical Engineering Congress and Exposition, pp. 113–120, 1997.
[12]
J. B. Bayat, Position analysis of planar tensegrity structures [Ph.D. thesis], University of Florida, Gainesville, Fla, USA, 2006.
[13]
M. Arsenault and C. M. Gosselin, “Kinematic and static analysis of a 3-PUPS spatial tensegrity mechanism,” Mechanism and Machine Theory, vol. 44, no. 1, pp. 162–179, 2009.
[14]
T. M. Tran, Reverse displacement analysis for tensegrity structures [M.S. thesis], University of Florida, Gainesville, Fla, USA, 2002.
[15]
M. Q. Marshall, Analysis of tensegrity-based parallel platform devices [M.S. thesis], University of Florida, Gainesville, Fla, USA, 2003.
[16]
M. Arsenault, “Stiffness analysis of a 2dof planar tensegrity mechanism,” Journal of Mechanisms and Robotics, vol. 3, no. 2, Article ID 021011, 2011.
[17]
S. Chen and M. Arsenault, “Workspace computation and analysis of a planar 2-DOF translational tensegrity mechanism,” in Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE '10), pp. 223–232, August 2010.
[18]
C. Sultan, M. Corless, and R. E. Skelton, “Tensegrity flight simulator,” Journal of Guidance, Control, and Dynamics, vol. 23, no. 6, pp. 1055–1064, 2000.
[19]
C. Sultan, M. Corless, and R. E. Skelton, “Peak to peak control of an adaptive tensegrity space telescope,” in Smart Structures and Materials, Mathematics and Control in Smart Structures, Proceedings of SPIE, pp. 190–201, March 1999.
[20]
C. Paul, F. J. Valero-Cuevas, and H. Lipson, “Design and control of tensegrity robots for locomotion,” IEEE Transactions on Robotics, vol. 22, no. 5, pp. 944–957, 2006.
[21]
C. Sultan and R. Skelton, “A force and torque tensegrity sensor,” Sensors and Actuators A: Physical, vol. 112, no. 2-3, pp. 220–231, 2004.
[22]
J. M. Mirats Tur and S. H. Juan, “Tensegrity frameworks: dynamic analysis review and open problems,” Mechanism and Machine Theory, vol. 44, no. 1, pp. 1–18, 2009.
[23]
M. Arsenault and C. M. Gosselin, “Static balancing of tensegrity mechanisms,” Journal of Mechanical Design, vol. 129, no. 3, pp. 295–300, 2007.
[24]
C. M. Gosselin, “Static balancing of spherical 3-DoF parallel mechanisms and manipulators,” International Journal of Robotics Research, vol. 18, no. 8, pp. 819–829, 1999.
[25]
S. M. M. Shekarforoush, M. Eghtesad, and M. Farid, “Design of statically balanced six-Degree-of-Freedom parallel mechanisms based on tensegrity system,” in Proceedings of the ASME International Mechanical Engineering Congress and Exposition (IMECE '09), pp. 245–253, November 2009.
