A Contribution to Gruebler’s Theory in the Number Synthesis of Plane Mechanisms

Abstract

A simple algorithm is introduced to solve Gruebler’s equation for constrained kinematic chains. Use of these criteria, however, brings clearly to the fore other problems, especially for mechanisms with negative or with two or more degrees of mobility. These are the related problems of mixed mobility and of independent parts within a linkage, which need to be solved, before any systematic process of exhaustive synthesis by automatic computer can be developed. A display of X = 2 mechanisms with up to nine members is also presented which is believed to be complete. Finally, the usefulness of the collection is described by showing how it can be applied to the design of a typewriter mechanism.