RESEARCH PAPERS: Design Automation Papers

Error Linearization in the Least-Squares Design of Function Generating Mechanisms

[+] Author and Article Information
D. J. Wilde

Mechanical Engineering Design, Stanford University, Stanford, California

J. Mech. Des 104(4), 881-884 (Oct 01, 1982) (4 pages) doi:10.1115/1.3256452 History: Received December 08, 1981; Online November 17, 2009


Minimum squared error mechanism synthesis can be done relatively easily by Error Linearization, a nonlinear regression procedure long known to statisticians. It has a descent property not possessed by the Newton-Raphson method, which consequently tends more readily to converge to unwanted stationary points. Applied to a four-bar function generator, error linearization yields, for the Freudenstein linear displacement equation, a least-squares design as a direct solution of three linear equations, whatever the number of design angle pairs. For the particular example considered, this design is mechanically unacceptable, but a good configuration is produced by a more natural nonlinear model in which angular error is the measure of performance. Here error linearization avoids nonoptimal local minima to which the Newton-Raphson method converges.

Copyright © 1982 by ASME
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