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TECHNICAL PAPERS

A Gröbner-Sylvester Hybrid Method for Closed-Form Displacement Analysis of Mechanisms

[+] Author and Article Information
A. K. Dhingra, A. N. Almadi, D. Kohli

Department of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53201

J. Mech. Des 122(4), 431-438 (Aug 01, 1999) (8 pages) doi:10.1115/1.1290395 History: Received August 01, 1999
Copyright © 2000 by ASME
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References

Morgan, A. P., 1987, Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems, Prentice Hall, New Jersey.
van Waerden, B. L., 1991, Algebra, Vols. 1 and 2, Springer Verlag, New York.
Buchberger, B., 1985, “Gröbner Bases: An Algorithmic Methods in Polynomial Ideal Theory,” in Multidimensional Systems Theory, N. K. Bose (ed), D. Reidel Publishing Company, Holland, pp. 184–232.
Macaulay, F. S., 1994, The Algebraic Theory of Modular Systems, Cambridge University Press, New York.
Mishra, B., 1993, Algorithmic Algebra, Springer Verlag, New York.
Roth, B., 1994, “Computational Advances in Robot Kinematics,” in Advances in Robot Kinematics and Computational Geometry, J. Lenarcic and B. Ravani (eds), Kluwer Academic Publishers, pp. 7–16.
Raghavan,  M., and Roth,  B., 1995, “Solving Polynomial Systems for the Kinematic Analysis and Synthesis of Mechanisms and Robot Manipulators,” Special 50th Anniv. Issue of the ASME J. Mech. Des., 117, pp. 71–79.
Dhingra, A. K., Kohli, D., and Xu, Y. X., 1992, “Direct Kinematics of General Stewart Platforms,” in Robotics, Spatial Mechanisms and Mechanical Systems, DE-Vol. 45, pp. 107–112.
Almadi, A. N., 1996, “On New Foundations of Kinematics Using Classical and Modern Algebraic Theory and Homotopy,” Ph.D. Thesis, University of Wisconsin-Milwaukee.
Husty,  M. L., 1996, “An Algorithm for Solving the Direct Kinematics of General Stewart-Gough Platforms,” Mech. Mach. Theory, 31, pp. 365–380.
Mourrain, B., 1993, “The 40 Generic Positions of a Parallel Robot,” in Proc. of the ACM-Intl. Symp. on Symbolic and Algebraic Computation, Kiev, Ukraine, pp. 173–182.
Lazard, D., 1993, “On the Representation of Rigid-Body Motions and its Applications to Generalized Platform Manipulators,” in Computational Kinematics, J. Angeles et al. (eds), pp. 175–181.
Wampler,  C. W., 1996, “Forward Displacement Analysis of General Six-in-Parallel SPS (Stewart) Platform Manipulators Using Soma Coordinates,” Mech. Mach. Theory, 31, pp. 331–337.
Raghavan,  M., 1993, “The Stewart Platform of General Geometry Has 40 Configurations,” ASME J. Mech. Des., 115, pp. 277–282.
Zhang,  C., and Song,  S. M., 1994, “Forward Displacement Analysis of Nearly General Stewart Platforms,” ASME J. Mech. Des., 116, pp. 54–60.
Innocenti,  C., 1994, “Analytical-Form Position Analysis of the 7-link Assur Kinematic Chain with Four Serially Connected Ternary Links,” ASME J. Mech. Des., 116, pp. 622–628.
Almadi, A. N., Dhingra, A. K., and Kohli, D., 1996, “Closed-Form Displacement Analysis of SDOF 8 Link Mechanisms,” in Proc. of ASME 1996 Design Engineering Technical Conf., Paper No. 96-DETC/MECH-1206.

Figures

Grahic Jump Location
A 6-DOF general Stewart mechanism
Grahic Jump Location
A loop of general Stewart mechanism
Grahic Jump Location
A 6-DOF general Stewart platform
Grahic Jump Location
A general 8-link 1-DOF mechanism

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