Solving a Planar Four-Bar Design Problem Using Continuation

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

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

J. Mech. Des 112(4), 544-550 (Dec 01, 1990) (7 pages) doi:10.1115/1.2912644 History: Received December 01, 1989; Online June 02, 2008


The problem of synthesizing a planar 4-bar with given pivots such that the coupler curve passes through five precision points is considered. It is shown that the design parameters must satisfy a system of 4 fourth-degree polynomial equations in 4 unknowns which has at most 36 nonzero real solutions. This polynomial system is solved using a continuation method, which thereby generates the collection of all designs that meet the precision-point specification. A computer program that implements this continuation method has been tested on a number of problems. It is reliable and fast enough for the purposes of design. The approach to kinematic design represented by this work is completely general, subject only to computer-time limitations that may arise for problems with many design elements.

Copyright © 1990 by The American Society of Mechanical Engineers
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