A New Isomorphism Identification Method For Kinematic Chain Based On Under-Triangle Matrix With Whole Information

Isomorphism identification is an indispensable part of kinematic chain(KC)structure synthesis,many isomorphism identification methods have been proposed by researchers.It is one of the goals of mechanism scholars to find isomorphic determination methods with simple and easy to understand determination principles,unobjectionable judgment results,and simple and efficient program design and computation.In this thesis,graph theory,mechanism topology and other related theories are applied to the study of mechanism.In order to solve the problem of isomorphism judgment of mechanism kinematic chain,a lower triangular matrix with whole information(LTMWI)is proposed,which can uniquely determine the structure of kinematic chain,based on the lower triangular matrix with whole information(LTMWI),the determination theorems of multiple joints and polygonal links are presented.Based on the principle that the lower triangular matrix with whole information(LTMWI)can uniquely express the structure of kinematic chain,a new isomorphism identification method,based on the exchange and compare of LTMWI is proposed.This method is based on the law of exchange of links’ numbers and key points’ numbers,by grouping the key points and increasing the coupling of the key points in the same group,the key points of a finite transformation matrix and the reference matrix are compared one by one to obtain the isomorphism determination results.The isomorphism identification method based on the LTMWI is compared with the minimum code method,Hamming number method and canonical adjacency matrix set in terms of computational complexity,and it is confirmed that the isomorphism identification method based on the LTMWI is more efficient.Based on the above theory,a new isomorphism identification method is proposed--a new isomorphism identification method for kinematic chain based on under-triangle matrix with whole information,which only needs to extract and categorize the information in the LTMWI and compare and analyze the elements between LTMWIs,without calculating the loops or eigenvalues and eigenvectors,etc.It is also demonstrated with a case that the computational complexity of the kinematic chain isomorphism determination method based on LTMWI is lower.The biggest advantage of this method is that the principle is easy to understand,the program design is simple,and the determination process only requires retrieval and comparison,which can quickly obtain the isomorphism determination results of kinematic chains.