Representation of planar kinematic chains with multiple joints based on a modified graph and isomorphism identification

The representation and isomorphism identification of kinematic chains (KCs) with multiple joints are crucial issues to be solved in mechanism research. In this paper, a modified graph—planar face graph (PF graph), is proposed. As a key concept, “face” has been put forward to represent the case that a single, specific relationship is incident with multiple incidents. Some other basic concepts relating to PF graph are also explained in detail. PF graph is used to represent KCs with multiple joints and it reflects the uniqueness of KCs and realizes the one-to-one correspondence between KCs and adjacency and incident matrices. It also establishes relationships with other methods for representing KCs and it is proved to be suitable for complex mechanical systems. Moreover, the sufficient and necessary condition of isomorphism are derived, and two properties of permutation similarity are analysed. Based on them, the modified eigenvalue eigenvector method and the maximum path method are proposed, and they are integrated to form a new algorithm. In addition, the reliability and efficiency of the algorithm are proved.