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Improved high-order adjacent vertex assignment sequence for similarity vertices and isomorphism identification of planar kinematic chains


 Isomorphism identification is fundamental to synthesis and innovative design of kinematic chains (KCs). The identification can be performed accurately by using the similarity of KCs. However, there are very few researches on isomorphism identification based on the properties of similarity vertices. In this paper, an improved high-order adjacent vertex assignment (IHAVS) sequence method is proposed to seek out the similarity vertices and identify the isomorphism of the planar KCs. First, the specific definition of IHAVS is described. Through the calculation of the IHAVS, the adjacent point value sequence reflecting the uniqueness of the structural features is established. Based on the value sequence, all possible similarity vertices, corresponding relations and isomorphism discrimination can be realized. By checking the topological diagrams of KCs of different number of links, the correctness of the proposed method are verified. Finally, the method is used to find the similarity vertices of all the 9-link 2-DOF(degree of freedom) planar KCs.