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

摘要： 同构判定是运动链型综合过程中一个关键步骤。提出了一种新的描述运动链信息的全息矩阵（MWI），以及基于此的复铰、多元构件判定原理。在全息下三角矩阵（LTMWI）可以确定运动链结构唯一性理论基础上，提出了一种全息下三角矩阵变换对比的同构判定新方法。该方法基于构件、关键点编号变换定律，将运动链表示为下三角全息矩阵并选定基准矩阵，通过关键点信息进行分组排列并将同组关键点非0元素前移，细分确定和待确定的关键点，在假定变换矩阵中所有关键点与基准矩阵中所有关键点位置逐一对应的情况下，对有限个变换矩阵与基准矩阵进行对比。该方法具有原理易于理解、程序设计容易、判定过程只需检索对比等优点，可快速获得两个运动链的同构判定结果。对多个运动链的分析结果表明了该方法的上述特点。

关键词: 同构判定, 全息矩阵, 基准矩阵, 多元复铰, 多元构件