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TECHNICAL PAPERS

Solving the Kinematics of Planar Mechanisms by Dixon Determinant and a Complex-Plane Formulation

[+] Author and Article Information
Charles W. Wampler

General Motors Research and Development Mail Code 480-106-359 30500 Mound Road Warren, Michigan 48090-9055e-mail: charles.w.wampler@gm.com

J. Mech. Des 123(3), 382-387 (Jul 01, 2000) (6 pages) doi:10.1115/1.1372192 History: Received July 01, 2000
Copyright © 2001 by ASME
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References

Wampler,  C., 1999, “Solving the kinematics of planar mechanisms,” ASME J. Mech. Des., 121, No. 3, pp. 387–391.
Nielsen,  J., and Roth,  B., 1999, “Solving the Input/Output Problem for Planar Mechanisms,” ASME J. Mech. Des., 121, No. 2, pp. 206–211.
Primrose,  E. J. F., Freudenstein,  F., and Roth,  B., 1967, “Six-bar Motion (Parts I–III),” Arch. Ration. Mech. Anal., 24, pp. 22–77.
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, No. 2, pp. 622–628.
Innocenti,  C., 1995, “Polynomial Solution to the Position Analysis of the 7-link Assur Kinematic Chain with One Quaternary Link,” Mech. Mach. Theory, 30, No. 8, pp. 1295–1303.
Han,  L., Liao,  Q., and Liang,  C., 2000, “Closed-Form Displacement Analysis for a Nine-Link Barranov Truss or a Eight-Link Assur Group,” Mech. Mach. Theory, 35, No. 3, pp. 379–390.
Dhingra,  A. K., Almadi,  A. N., and Kohli,  D., 1999, “A Framework for Closed-Form Displacement Analysis of Planar Mechanisms,” ASME J. Mech. Des., 121, No. 3, pp. 392–401.
Lösch, S., 1995, “Parallel Redundant Manipulators Based on Open and Closed Normal Assur Chains,” Computational Kinematics, J.-P. Merlet and B. Ravani, eds., Kluwer Academic Publ., Dordrecht, The Netherlands, pp. 251–260.
Dhingra,  A. K., Almadi,  A. N., and Kohli,  D., 2000, “A Gröbner-Sylvester Hybrid Method for Closed-Form Displacement Analysis of Mechanisms,” ASME J. Mech. Des., 122, No. 4, pp. 431–438.
Wampler,  C., Morgan,  A., and Sommese,  A., 1990, “Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics,” ASME J. Mech. Des., 112, No. 1, pp. 59–68.
Wampler, C., 1996, “Isotropic Coordinates, Circularity, and Bezout Numbers: Planar Kinematics from a New Perspective,” Proc. ASME Des. Eng. Tech. Conf., Aug. 18–22, Irvine, CA, Paper 96-DETC/Mech-1210.
Waldron,  K. J., and Sreenivasen,  S. V., 1996, “A Study of the Solvability of the Position Problem for Multi-Circuit Mechanisms by Way of Example of the Double Butterfly Linkage,” ASME J. Mech. Des., 118, No. 3, pp. 390–395.
Shen,  H., Ting,  K.-L., and Yang,  T., 2000, “Configuration Analysis of Complex Multiloop Linkages and Manipulators,” Mech. Mach. Theory, 35, No. 3, pp. 353–362.
Dixon,  A. L., 1909, “The Eliminant of Three Quantics in Two Independent Variables,” Proc. London Math. Soc., Ser. 2, 7, pp. 49–69.

Figures

Grahic Jump Location
Double-butterfly mechanism
Grahic Jump Location
Input/output and tracing curve equivalence

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