基于全息下三角矩阵变换对比的运动链同构判定方法

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中图分类号：TH112

DOI：10.3969/j.issn.1004-132X.2025.06.005 开放科学（资源服务）标识码（OSID）：

Isomorphism Identification Method for Kinematic Chain Based on Exchange and Comparison of Lower Triangular Matrix with Whole Information

ZHANG Guangshuai SUN Liangbo*LIU Xiaocui ZHANG Deping ZHOU Huaxi School of Mechanical Engineering，Wuhan Polytechnic University，Wuhan，430023

Abstract： Isomorphism identification was recognized as a critical step in the synthesis processes of kinematic chains（KC）. A new MWI was proposed to describe the structural information of KCs. The principles for determining multiple-joint and polygonal links were introduced. Based on the principle that the lower triangular matrix with whole information（LTMWI）may uniquely express the structure of KCs，a new isomorphism identification method was proposed with the comparison and exchange of LTMWI. This method relied on the transformation law of links and key point numbers. Two KCs were expressed by LTMWI，with one LTMWI was selected as the datum matrix. After grouping the key points and moving the non-zero elements of key points in the same group forward，the determined key points and the key points to be determined were obtained. Under the assumption that all key points in the exchange matrix correspond one-to-one with the key point positions in the datum matrix， a finite number of exchange matrices were compared. The method has advantages such as a simple principle，ease of programming，and an identification process requiring only retrieval/comparison operations. It could quickly provide isomorphism identification results，and the mapping of links and even revolute pairs could be obtained. Isomorphism analyses of several KCs demonstrate the aforementioned characteristics of the method.

Key words： isomorphism identification；matrix with whole information（MWI）；datum matrix; multiple-joint；polygonal link

0 引言

机构运动链构型综合是机构学领域的一个难题，也是机构创新设计的核心研究内容[1]。（剩余13332字）