Optimum Synthesis of Two-Degree-of-Freedom Planar and Spatial Function Generating Mechanisms Using the Penalty Function Approach

This paper presents the synthesis of two-degree-of-freedom function generating mechanisms as a mathematical programming problem. The optimum set of dimensions of a mechanism are determined using a penalty function approach. Also, a new algorithm is developed for finding the first mechanism satisfying all inequality constraints to serve as an initial approximation. A single objective function as well as the equality and inequality constraints are expressed explicitly from conditions of linkage closure, mobility, and transmissibility. The method is demonstrated through an example for a spatial RSSRP function generating mechanism.