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.
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December 1990
Research Papers
Solving a Planar Four-Bar Design Problem Using Continuation
A. P. Morgan,
A. P. Morgan
Mathematics Department, General Motors Research Laboratories, Warren, Michigan 48090
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C. W. Wampler, II
C. W. Wampler, II
Mathematics Department, General Motors Research Laboratories, Warren, Michigan 48090
Search for other works by this author on:
A. P. Morgan
Mathematics Department, General Motors Research Laboratories, Warren, Michigan 48090
C. W. Wampler, II
Mathematics Department, General Motors Research Laboratories, Warren, Michigan 48090
J. Mech. Des. Dec 1990, 112(4): 544-550 (7 pages)
Published Online: December 1, 1990
Article history
Received:
December 1, 1989
Online:
June 2, 2008
Citation
Morgan, A. P., and Wampler, C. W., II (December 1, 1990). "Solving a Planar Four-Bar Design Problem Using Continuation." ASME. J. Mech. Des. December 1990; 112(4): 544–550. https://doi.org/10.1115/1.2912644
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