Identifying and Counting the Number of Mechanisms From Kinematic Chains Subject to Design Constraints

Abstract

An approach is presented, based on combinatorial theory, for the complete enumeration of nonisomorphic mechanisms precisely from kinematic chains. And, based on the permutation groups, the concept of the generating function, and Polya’s Theory, mathematical expressions are derived for counting the number of the identified mechanisms subject to the design constraints of the adjacent/incident relationship among links, joints, or links and joints. Examples are provided to illustrate the proposed approach. The results of this work can instead of the observation method to inspect the isomorphism for mechanisms; furthermore, all nonisomorphic mechanisms can be obtained exactly and systematically.