运动链拓扑胚图的同构判断

平面并联机构基于胚图的综合方法中,拓扑胚图的同构判断是关键的环节。针对不含二元杆的运动链拓扑胚图,解决它们之间的同构判断问题。运动链的拓扑胚图与拓扑图相比有着独特的个性,由于在支链上没有二元点,所以图的顶点之间的关系主要是顶点之间的相对位置。根据拓扑胚图的特性,从关于图的邻接矩阵的经典理论出发,建立图的任意顶点之间的路径数矩阵,将路径数矩阵的元素按照一定规则排列成路径数组。论证了拓扑胚图同构的条件。在度序列和一阶路径数组相等的前提下,利用二阶路径数组来判断拓扑胚图是否同构。举实例说明判断过程及具体应用。拓扑胚图同构判断问题的解决不仅为基于胚图的型综合奠定了基础,而且对于某些运动链拓扑图的同构判断也具有普遍意义。

Isomorphism Identification of Kinematic Chain Topology Embryonic Graphs

Isomorphism identification of topology embryonic graphs is a key link in plane parallel mechanism synthesis methods based on embryonic graph.Aiming at kinematic chains topology embryonic graph without binary links,the problem of isomorphism identification among them is solved.Topology embryonic graph has unique feature against topology graph.Because there aren’t binary vertices in limbs of topology embryonic graph,relation among vertices are largely relative position among them.According to the feature of topology embryonic graph,the matrix of path number among any vertices of topology embryonic graph is set up from the classical theory of adjacency matrix about graph.The items of the path number matrix are arranged into path array according to certain rule.The isomorphic condition for topology embryonic graphs is demonstrated.Topology embryonic graphs are identified if they are isomorphic by second order path array when degree sequence and first order path array are same.Examples are given to illustrate identification procedure and specific application.Solution to the problem of isomorphism identification of topology embryonic graph not only lays the foundation for type synthesis based on embryonic graph,but also there is universal significance for isomorphism identification of some kinematic chain topology graphs.