Abstract
The quality index for a redundant 4–41 in-parallel manipulator with a square platform and a square base was obtained previously. In this paper the optimum quality index for a redundant 4–8 manipulator is determined. The device has a square platform and an octagonal base connected by eight legs. The quality index is a dimensionless ratio which takes a maximum value of 1 at a central symmetrical configuration that is shown to correspond to the maximum value of the square root of the determinant of the product of the manipulator Jacobian by its transpose. The Jacobian matrix is none other than the normalized coordinates of the eight leg lines. It is shown that the quality index can be used as a constructive measure of not only acceptable and optimum design proportions but also an acceptable operating workspace.
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References
Dasgupta, B. and Mruthyunjaya, T.S. (1998). Force redundancy in parallel manipulators: theoretical and practical issues. Mechanism and Machine Theory, Vol. 33, No. 6, pp. 727–742.
Gosselin, C. and Angeles, J. (1988). The optimum kinematic design of a planar three-degree-of-freedom parallel manipulator. ASME Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 110, No. 3, pp. 35–41.
Gosselin, C. and Angeles, J. (1989). The optimum kinematic design of a spherical three-degree-of-freedom parallel manipulator. ASME Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 111, No. 6, pp. 202–207.
Lee, J., Duffy, J., and Keler, M. (1996). The optimum quality index for the stability of in-parallel planar platform devices. Proceedings of the ASME 24th Biennial Mechanisms Conference, Irvine, Ca., USA, 96-DETC/MECH-1135.
Lee, J., Duffy, J., and Hunt, K.H. (1998). A practical quality index based on the octahedral manipulator. The International Journal of Robotics Research, Vol. 17, No. 10, pp. 1081–1090.
Lee, J. and Duffy. J. (1999). The optimum quality index for some spatial in-parallel devices. 1999 Florida Conference on Recent Advances in Robotics, Gainesville, FL, USA.
Merlet, J.P. (1996). Redundant parallel manipulators. Laboratory Robotics and Automation, Vol. 8, No. 1, pp. 17–24.
White, N. and Whiteley, W. (1983). The algebraic geometry of stresses in frameworks. S.I.A.M. Journal of Algebraic and Discrete Methods, Vol. 4, No. 4, pp. 481–511.
Zanganeh, K.E. and Angeles, J. (1997). Kinematic isotropy and the optimum design of parallel manipulators. The International Journal of Robotics Research, Vol. 16, No. 2, pp. 185–197.
Zhang, Y. and Duffy, J. (1998). The optimum quality index for a redundant 4–4 in-parallel manipulator. RoManSy 12: Theory and Practice of Robots and Manipulators, Proceedings of the Twelfth CISM-IFToMM Symposium, Paris, pp. 289–296.
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© 2000 Springer Science+Business Media Dordrecht
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Zhang, Y., Duffy, J., Crane, C. (2000). The Optimum Quality Index for a Spatial Redundant 4–8 in-Parallel Manipulator. In: Lenarčič, J., Stanišić, M.M. (eds) Advances in Robot Kinematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4120-8_25
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DOI: https://doi.org/10.1007/978-94-011-4120-8_25
Publisher Name: Springer, Dordrecht
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