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.
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October 1982
Research Papers
Error Linearization in the Least-Squares Design of Function Generating Mechanisms
D. J. Wilde
D. J. Wilde
Mechanical Engineering Design, Stanford University, Stanford, California
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D. J. Wilde
Mechanical Engineering Design, Stanford University, Stanford, California
J. Mech. Des. Oct 1982, 104(4): 881-884 (4 pages)
Published Online: October 1, 1982
Article history
Received:
December 8, 1981
Online:
November 17, 2009
Citation
Wilde, D. J. (October 1, 1982). "Error Linearization in the Least-Squares Design of Function Generating Mechanisms." ASME. J. Mech. Des. October 1982; 104(4): 881–884. https://doi.org/10.1115/1.3256452
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