Formulating an Invariant Manipulability Index of Gough-Stewart Platform

Abstract:

Manipulability indexes have been extensively used as objective functions or constraints in the optimal design of robots, especially for the robots with pure active joints and the end-effectors only involving positioning or orientation. The moving platform of Gough-Stewart platform can involve both positioning and orientation, which leads to the conventional Jacobian matrix with entries bearing disparate physical units, then the established manipulability index based on the conventional Jacobian matrix has no physical meaning and is variable under a change of units. Based on a dimensionless Jacobian matrix, this paper established a new manipulability index, which has physical meaning and is invariant under a change of units. In order to design a good performance motion simulator, the extreme values of the new and old manipulability indexes of 2 commercial flight simulators in their reachable workspaces were found by random search method, respectively. From the results, the extreme values of the new manipulability index are in regularity, and can be used as references in the optimal design of the Gough-Stewart platform as motion simulator.

• Periodical: Advanced Materials Research (Volumes 479-481)
• Pages: 2321-2326
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.479-481.2321
• Online since: February 2012
• Authors: Guo Jun Liu, Shu Tao Zheng, Xiao Chu Liu, Ying Bo Wang, Jun Wei Han
• Keywords: Gough-Stewart Platform, Homogeneous Jacobian Matrix, Manipulability Index, Optimal Design, Random Search

References

[1] J.P. Merlet: Parallel Robots (Second Edition) (Springer, Netherlands, 2006), pp.70-93

[2] F. Hao, J.P. Merlet: Mechanism and Machine Theory, Vol.40 (2005) No.2, pp.157-171

[3] J. Angeles, F. C. Park: in B. Siciliano , O. Khatib (editors), Handbook of Robotics. (Springer,Berlin-Heidelberg, 2008), pp.229-244

[4] Ou Ma, J. Angeles: Fifth International Conference on Advanced Robotics (Pisa, Italy, Jun, 1991), pp.1130-1135

[5] K. E. Zanganeh, J. Angeles: International Journal of Robotics Research, Vol.16 (1997) No.2, pp.185-197

[6] A. Fattah , Ghasemi A. M.Hasan: International Journal of Robotics Research, Vol.21 (2002) No.9, pp.811-824

[7] C. M. Gosselin: Robotics and Autonomous Systems, Vol.9 (1992) No.4, pp.213-226

[8] S. G. Kim, J. Ryu: IEEE Transactions on Robotics and Automation, Vol.19 (2003) No.4 , pp.731-737

[9] S. Bandyopadhyay, A.Ghosal: Mechanism and Machine Theory, Vol.43 (2008) No.5, pp.591-616

[10] T.Yoshikawa : International Journal of Robotics Research, Vol.4 (1985) No.2 , pp.3-9

[11] T.Yoshikawa : Journal of Robotic Systems. Vol.2 (1985) No.1, pp.113-124,.

[12] K. L. Doty, C. Melchiorri, E. M. Schwartz, C. Bonivento: IEEE Transactions on Robotics and Automation, Vol.11 (1995) No.3, pp.462-468

DOI: 10.1109/70.388791

[13] J. P. Merlet: Journal of Mechanical Design, Vol.128 (2006) No.1, pp.199-206

[14] J. P. Merlet, D. Daney: in Wang Lihui, Xi Jeff (editors), Smart Devices and Machines for Advanced Manufacturing. (Springer, London, 2008), pp.1-25

[15] J. C. David, B. B. Richard: AIAA Modeling and Simulation Technologies Conference and Exhibit (Providence, Rhode Island, August 2004) , pp.1-10

[16] Liu Guo-jun, Zheng Shu-tao, Han Jun-wei: Journal of South China University of Technology (Natural Science), Vol.39 (2011) No.4, pp.70-75 (in Chinese)

[17] L. W. Tsai: Journal of Mechanical Design, Vol.122 (2000) NO.3, pp.3-9

[18] Tunchan Cura: International Journal of Contemporary Mathematical Sciences, Vol.5 (2010) No.4, pp.179-190

[19] Ou Ma: Mechanical Analysis of Parallel Manipulators with Simulation, Design and Control Applications (Ph.D., McGill University, Canada 1991), pp.256-258