用拓扑特性矩阵辨识运动链的同构体及机架变换研究

IDENTIFICATION OF ISOMORPHISM AND INVERSIONS OF KINEMATIC CHAINS USING LOOP-LINK-JOINT-MATRIX

基于运动链的基本环路及环路中构件、运动副的互相连接关系，建立了描述平面和空间运动链及机构的拓扑特性矩阵，对平面、空间运动链及机构的同构体辨识问题进行了研究。由于拓扑特性矩阵较常用于同构体辨识的邻接矩阵、关联矩阵等矩阵的元素少，而且可以通过比较拓扑特性矩阵的对应行列的元素直接进行同构体的辨识，因此，应用拓扑特性矩阵辨识同构体是更简便和高效的。给出了应用拓扑特性矩阵辨识同构体的方法、步骤及流程图，并给出了较典型的辨识例子（包括空间运动链），证明了该方法的正确性和高效性。同时还应用拓扑特性矩阵对运动链的机架变换问题进行了研究。

The structural characteristics of both planar and spatial kinematic chains are described by proposing a new topological presentation, which is called loop-link-joint-matrix (shortened as JLL), based on independent loop(s) of kinematic chains. JLL has fewer elements compared with common used structural characteristic matrix and characteristic polynomial in the literature and JLL can be easy formed. JLL is applied to identify isomorphism of both planar and spatial kinematic chains and mechanisms with all kinds of joints by comparing the corresponding elements of JLL in rather simpler way. Method, procedures and flow chart of identification are presented. It is also capable of studying the inversion problems of kinematic chains and mechanisms by JLL. Examples of both detecting isomorphism and inversion problems are given.