Generating functions for mechanism specialization

This paper proposes an innovative mathematical method for generating specialized mechanisms without having to check for isomorphic mechanisms. Specifically, using the basic permutation group types, the analysis derives four generating functions and four mathematical operators, which it then uses to generate complex generating functions for six- and eight-link specialized mechanisms that can be classified based on a link or a joint permutation group. Because each function is a polynomial in which every term is a specialized mechanism, there is no need to inspect for isomorphism. The accuracy and efficiency of the method is verified using numerical examples and Polya's theory.