Singularity Loci of Actuation Schemes for 3RRR Planar Parallel Manipulator

Authors: S. Ramana Babu, V. Ramachandra Raju, K. Ramji

Abstract:

This paper presents the effect of actuation schemes on the performance of parallel manipulators and also how the singularity loci have been changed in the reachable workspace of the manipulator with the choice of actuation scheme to drive the manipulator. The performance of the eight possible actuation schemes of 3RRR planar parallel manipulator is compared with each other. The optimal design problem is formulated to find the manipulator geometry that maximizes the singularity free conditioned workspace for all the eight actuation cases, the optimization problem is solved by using genetic algorithms.

Keywords: Actuation schemes, GCI, genetic algorithms.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1125025

References:

[1] C. M. Gosselin and J. Angles, “Singularity analysis of closed loop kinematic chains,” IEEE Transactions on Robotics and Automation, vol.6 (3), pp. 15–64, Jan. 1990.
[2] J.P. Merle, “Redundant parallel manipulators,” Laboratory Robotics and Automation, vol.8 (1), pp.17-24, July 1996.
[3] S.H. Cha, T.A. Lasky and S.A. Velinsky, “Singularity avoidance for the 3RRR mechanism using kinematic Redundancy,” in Proc. 4th Annu. Allerton Conf. Robotics and Automation, New York, 2007, pp. 1195–2000.
[4] M.G. Mohamed and C.M. Gosselin, “Design and analysis of kinematically redundant parallel manipulators with configurable platforms,” IEEE Transactions on Robotics, vol.21 (3), pp.277-287, jan.2005.
[5] O. Alba-Gomez, P. Wenger and A. Pamanes, “Consistent kinetostatic indices for planar parallel manipulators: Application to the optimal kinematic inversion,” in Proc. 4th Annu. Allerton Conf. IDETC/CIE, New York, 2005, pp. 1195–2000.
[6] V. Arakelian, S. Briot and V. Glazunov, “Increase in singularity-free zones in the workspace of parallel manipulators using mechanisms variable structure.” Mechanism and Machine theory, vol.43 (9), pp.1129-1140, 2008.
[7] H.J. Su, P. Dietmaier and J.M. Macarthy, “Trajectory planning for constrained parallel manipulators,” ASME Journal of Mechanical Design, vol.125 (1), pp.709-716, 2003.
[8] I. Ebrahimi, J.A. Carretero and R. Boudreau, “3PRRR redundant planar parallel manipulator: inverse displacement, workspace and singularity analyses,” Mechanism and Machine theory, vol.42 (8), pp.1007-1016, 2007.
[9] N. Rakotomanga, D. Chablat and S. Caro, “Kinetostatic performance of a planar parallel mechanism with variable actuation,” Advances in robot kinematics: analysis and design, vol.21, pp.311-320, 2008.
[10] F. Firamani and P. Podhorodeski, “Forced unconstrained poses for a redundantly actuated planar parallel manipulator,” Mechanism and Machine Theory, vol.39, pp.459-476, 2004.
[11] F. Firmani and P. Podhorodeski, “Singularity analysis of a planar parallel manipulators based on forward kinematic solutions,” Mechanism and Machine Theory, vol.44, pp.1386-1399, 2009.
[12] X-J. Liu, J.S. Wang and F. Gao, “Performance atlases of the workspace for planar 3-DOF parallel manipulators,” Robotica, vol.18 (5), pp.563-568, 2000.
[13] F. Gao, X-J. Liu and X. Chen, “The relationship between the shapes of the workspace and the link lengths of 3-DOF symmetrical planar parallel manipulators, “Mechanism and Machine Theory, vol.36 (2), pp.205-220, 2001.
[14] D. Chablat and P. Wenger, “The kinematic analysis of a symmetrical three-degrees-of-freedom planar parallel manipulator, in Conf. Rec. 2004 World Academy of Science, Engineering and Technology Int. Conf. Robot design, dynamics and control, pp. 1–7.
[15] J. Kotlarski, B. Heimann and T. Ortmaier, “Improving the pose accuracy of a planar 3RRR parallel manipulator using kinematic redundancy and optimized switching patterns,” in Conf. Rec. 2008 IEEE Int. Conf. Robotics and Automation, pp. 3863–3868.
[16] E.A.B. Lomonova and J.A. Andre, “Optimiation of contact less planar actuator with manipulator,” IEEE T Magn, vol.44, pp.1118-1121, 2008.
[17] J. Holland, “Adaptation in natural and artificial systems, The University of Michigan press, Ann Arbor MI, 1975.
[18] G. Alici and B. Shirinadesh, “Optimum synthesis of planar parallel manipulators based on kinematic isotropy and force balancing,” Robotica, vol.22, pp.97-108, 2004.
[19] M. Ceccarelli, G. Carbone and F. Ottaviano, “An optimization problem approach for designing both serial and parallel manipulators,” in Proc. MUSME International symposium multibody systems and mechatronics, Uberlandia, 2005, pp. 6-9.
[20] C. Gosselin and J. Angeles. “A Global performance index for kinematic optimization of robotic manipulators,” ASME Journal of Mechanical Design, vol.113, pp.220-226, 1991.