Nonlinear optimization of planar linkages for kinematic syntheses

Abstract

In the present article a method is proposed for the optimum synthesis of planar mechanisms with lower pairs and a configuration of any type. It is valid for path synthesis generation, connecting-rod guidance, function generation, and any combination on the same mechanism. The idea is to start out with a mechanism of given dimensions that is required to satisfy the synthesis conditions, allowing the deformation of its component elements. The mechanism that least needs to be deformed will be the optimum according to this criterion. The parameters of the resulting error function are the lengths of the binary elements, the triple dimensions in the tertiaries, and the positions of the nodes linked to the frame. An expansion is used in which the first and second derivatives of the error function are calculated without the use of finite-difference schemata. This expansion enables one to use a Newton method, results of which are optimized by means of linear search, and facilitates better solutions with very few iterations. © 1995.