Complete Solution of the Nine-Point Path Synthesis Problem for Four-Bar Linkages

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

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

A. J. Sommese

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

J. Mech. Des 114(1), 153-159 (Mar 01, 1992) (7 pages) doi:10.1115/1.2916909 History: Received November 01, 1990; Online June 02, 2008


The problem of finding all four-bar linkages whose coupler curve passes through nine prescribed points has been a longstanding unsolved problem in kinematics. Using a combination of classical elimination, multihomogeneous variables, and numerical polynomial continuation, we show that there are generically 1442 nondegenerate solution along with their Roberts cognates, for a total of 4326 distinct solutions. Moreover, a computer algorithm that computes all solutions for any given nine points has been developed.

Copyright © 1992 by The American Society of Mechanical Engineers
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