Similar Vertices and Isomorphism Detection for Planar Kinematic Chains Based on Ameliorated Multi-Order Adjacent Vertex Assignment Sequence

Abstract

Isomorphism detection is fundamental to the synthesis and innovative design of kinematic chains (KCs). The detection can be performed accurately by using the similarity of KCs. However, there are very few works on isomorphism detection based on the properties of similar vertices. In this paper, an ameliorated multi-order adjacent vertex assignment sequence (AMAVS) method is proposed to seek out similar vertices and identify the isomorphism of the planar KCs. First, the specific definition of AMAVS is described. Through the calculation of the AMAVS, the adjacent vertex value sequence reflecting the uniqueness of the topology features is established. Based on the value sequence, all possible similar vertices, corresponding relations, and isomorphism discrimination can be realized. By checking the topological graph of KCs with a different number of links, the effectiveness and efficiency of the proposed method are verified. Finally, the method is employed to implement the similar vertices and isomorphism detection of all the 9-link 2-DOF(degree of freedom) planar KCs.

A synthesis method for planetary gear trains based on new topological model and similarity

“…Then, as the core of structural synthesis, isomorphism identification aims to exclude repeated structure types. Many scholars have proposed various isomorphism identification methods for PGTs, such as loop algebra theory [13,22], displacement group theory [23], multi-order adjacent vertex assignment sequence [24], equivalent resistance matrix [25], and vertex correlation polynomial and vertex distance [26][27], topological index [28], and modified eigenvalue eigenvector [29].…”