Abstract: The adjacent relation of mechanism kinematic chain is represented by a primary adjacency matrix by using primes to mark its components. An isomorphism identification matrix results from the primary adjacency matrix and prime products representing secondary adjacent relation, and uses its determinant and solution vector of linear equation system to identify mechanism isomorphism. Dynamically, the identification matrix is modified by new primes on the basis of the classification of solution vector elements. The result generates a solution vector with independent elements, which determines the positions of all nodes in the topological graph of a kinematic chain. Furthermore, a mapping relation, which results in a necessary and sufficient condition for isomorphism, is established between componential codes of two isomorphic mechanisms. As a result, this new identification method utilizes varying primes to virtually destruct the symmetry of the topological graph and change local and secondary adjacency relations among nodes under unchanged topological structure. Then, this method is also available for isomorphism identification of general undirected graphs. Applied examples show that it is very effective and reliable for automatic identification with code mapping of isomorphism mechanisms and polynomial algorithm for computation time.

Key words: Adjacency matrix, Isomorphism identification, Kinematic chain, Linear equation system, Prime, Solution vector