一种基于汉明矩阵的运动链同构识别方法

A Method for Isomorphism Recognition of Kinematic Chains Based on the Hamming Matrix

基于汉明矩阵提出了一种新的同构识别方法,此方法首先以连杆邻接矩阵为已知量导出汉明矩阵,然后计算汉明矩阵的平方阵且将平方阵的主对角线元素置为零,接着求解该平方阵的特征值,最后将特征值与拓扑因子的乘积求和得出运动链拓扑图的同构识别码(Recognition code,RC)。此识别码是运动链拓扑图的一个不变量,它不随着图中顶点标号的变化而变化。若两拓扑图的同构识别码相同,则它们是同构的,否则是异构的。此方法的有效性已通过实例得以证明。这种方法简单、高效且便于计算机编程,为机械结构设计中的同构识别提供了一种有力工具。

To improve the efficiency of the mechanical design,it is necessary to eliminate the isomorphic kinematic chains.Based on the Hamming matrix,a novel method for the isomorphism recognition is proposed in this paper.Firstly,the Hamming matrix is derived from the adjacency matrix which is the only known quantity needed for the method.Secondly,the Hamming matrix is squared to obtain a square matrix and the angular elements in the square matrix are placed to zero.Thirdly,the eigenvalues of the square matrix are calculated,and then the isomorphic recognition code.(called RC)of the topological graph of kinematic chains is obtained by summing the product of eigenvalues with the topological factor.This recognition code is an invariant,and it does not vary with the vertex label in the graph.When the isomorphism recognition code of the two topological graphs is the same,they are isomorphic,otherwise they are not.The effectiveness of this method has been proved by examples.This method is simple,efficient and easy for computer program,which makes it become a new powerful tool for isomorphic recognition in mechanical configuration design.