Improved approach for counting the number of mechanisms from kinematic chains subject to design constraints

An improved approach is proposed, based on combinatorial theory, for counting the number of identified mechanisms from kinematic chains. A procedure for obtaining the defined modified permutation groups is presented. By applying the variables to indicate the remaining links or joints in the modified permutation groups, and based on the concepts of generating function and Polya's Theory, a pattern inventory polynomial is developed to identify the results for the structural synthesis of identified mechanisms subject to design constraints. Three examples are provided to illustrate the proposed approach. The results of this work can replace the observation method to inspect the isomorphism for mechanisms.