Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics

[+] Author and Article Information
C. W. Wampler, A. P. Morgan

Mathematics Department, General Motors Research Laboratories, Warren, MI 48090

A. J. Sommese

Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556

J. Mech. Des 112(1), 59-68 (Mar 01, 1990) (10 pages) doi:10.1115/1.2912579 History: Received February 01, 1989; Online June 02, 2008


Many problems in mechanism design and theoretical kinematics can be formulated as systems of polynomial equations. Recent developments in numerical continuation have led to algorithms that compute all solutions to polynomial systems of moderate size. Despite the immediate relevance of these methods, they are unfamiliar to most kinematicians. This paper attempts to bridge that gap by presenting a tutorial on the main ideas of polynomial continuation along with a section surveying advanced techniques. A seven position Burmester problem serves to illustrate the basic material and the inverse position problem for general six-axis manipulators shows the usefulness of the advanced techniques.

Copyright © 1990 by The American Society of Mechanical Engineers
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