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

Abstract

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.