Coupler-Point-Curve Synthesis Using Homotopy Methods

[+] Author and Article Information
Lung-Wen Tsai, Jeong-Jang Lu

Mechanical Engineering Department and Systems Research Center, University of Maryland, College Park, MD 20742

J. Mech. Des 112(3), 384-389 (Sep 01, 1990) (6 pages) doi:10.1115/1.2912619 History: Online June 02, 2008


A numerical method called “Homotopy Method” (or Continuation Method) is applied to the problem of four-bar coupler-curve synthesis. We have shown that: for five precision points, the “General Homotopy Method” can be applied to find the link lengths of number of four-bar linkages, and for nine precision points, a heuristic “Cheater’s Homotopy” can be applied to find some four-bar linkages. The nine-coupler-points synthesis problem is highly non-linear and highly singular. We have found that Newton-Raphson’s method and Powell’s method tend to converge to the singular solutions or do not converge at all, while the Cheater’s Homotopy always finds some non-singular solutions although sometimes the solutions may be complex.

Copyright © 1990 by The American Society of Mechanical Engineers
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