A methodology is presented, based on combinatorial theory, for the enumeration of non-isomorphic mechanisms precisely from kinematic chains. According to the defined permutation groups, an algorithm for generating all non-isomorphic identified mechanisms by assigning various types of links and joints to kinematic chains is proposed. Based on the concepts of Polya’s theory and generating function, mathematical expressions are derived for counting the number of the identified mechanisms subject to the design constraints of adjacent/incident relationship between links and joints. Examples are provided to illustrate the proposed approach.

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