运动链拓扑图的特征数组表示及同构判断  

Character Arrays Representation and Isomorphism Identification of Kinematic Chain Topology Graphs

作　　者：丁玲[1] 路懿[2] 

机构地区：[1]燕山大学信息科学与工程学院,秦皇岛066004 [2]燕山大学机械工程学院,秦皇岛066004

出　　处：《机械工程学报》2010年第7期63-67,共5页Journal of Mechanical Engineering

基　　金：教育部博士学科点专项科研基金资助项目(20060216006)

摘　　要：运动链拓扑图同构判断是一个世界性的难题,为解决它提出新的方法。基于运动链拓扑图的特点,用特征数组来描述运动链的拓扑图。将运动链拓扑图支链上的二元杆数按照多元杆进行分组排列,组内的各支链顺序可变,组外的各多元杆的顺序可变,从而形成特征数组。用特征数组来描述拓扑图的特征,这一描述方式直观简洁且不受拓扑图画法形式和标号方式变化的影响。借用字符串的概念定义特征数组的同构,用Visual Basic编程,给出程序实现原理。建立判断矩阵来判断同构的特征数组,只有当判断矩阵的每行和、每列和同时为非零值时,两拓扑图是同构的。最后通过实例证明该方法准确、简单、高效且易于在计算机上实现。同构判断问题的解决为机构型综合奠定了基础。Isomorphism identification of kinematic chain topology graphs is a world puzzle. A new approach is presented to solve it. Kinematic chain topology graphs are depicted with character arrays based on the characteristic of kinematic chain topology graphs. The number of binary links in the limbs of topology graphs is arranged in group according to links with multi points of connection. The order of limbs in the groups can change and the order of links with multi points of connection outside the groups also can change, thereby forming character arrays. Characteristic of topology graphs is depicted with character arrays. This representation is straightforward and not affected when drawing modes and labeling ways change in topology graphs. Isomorphism of character arrays is defined in virtue of the concept of character string. The realization principle of program with Visual Basic is presented. Identification matrix is constructed to identify isomorphic character arrays. Two topology graphs are isomorphic only when the sum of every row and the sum of every column in identification matrix are nonzero simultaneously. Finally, case study proves that the approach is accurate, simple, efficient and easy to realize on a computer. The solution of the problem of isomorphism identification lays a foundation for mechanism type synthesis.

关 键 词：拓扑图 特征数组 判断矩阵 同构判断 

分 类 号：TH112[机械工程—机械设计及理论] TP391[自动化与计算机技术—计算机应用技术]