一种基于汉明矩阵和连杆邻接矩阵的运动链同构识别方法

A Method for Isomorphism Recognition of Kinematic Chain based on the Hamming Matrix and Connecting Rod Adjacency Matrix

在机械装置的创造性设计中,应淘汰同构运动链,为后续设计减少机构方案,提高机械装置的设计效率。基于汉明矩阵提出了一种新的运动链同构判别方法。首先,从连杆邻接矩阵中导出运动链汉明矩阵;接着,将汉明矩阵的平方阵与连杆邻接矩阵的立方阵求积,得到运动链积矩阵;然后,将积矩阵各行元素以降序排列得积矩阵行序列;最后,将行序列中各元素与本文中所定义的拓扑因子相乘并求总和,得出运动链的同构识别码,即IRC(Isomorphism recognition code)。同构识别码不随构件标号的改变而改变,故若运动链的同构识别码相同,则它们为同构链,否则为异构链。大量实例证明了该方法的有效性。因其简洁、高效且利于计算机执行的特点,故可以考虑将其作为同构筛选的一种新的选择。

In the creative design of mechanical devices,the isomorphic kinematic chains should be elimi⁃nated to reduce the mechanism scheme for subsequent design and improve the design efficiency of mechanical device.A new method for isomorphism recognition of kinematic chains is proposed based on the Hamming ma⁃trix.Firstly,the Hamming matrix of kinematic chains is educed from the link adjacency matrix,then the square matrix of Hamming matrix and the cubic matrix of link adjacency matrix are integrable to obtain the product ma⁃trix of kinematic chains.Secondly,the elements of each row in the product matrix are ordered in descending to get the row sequences of the product matrix.Finally,the isomorphism recognition code(IRC)of the kinematic chain is obtained by the sum of the product of the element in the row sequence with the defined topological fac⁃tor.The isomorphism recognition code does not change with the link labels,so if the isomorphism recognition codes of the kinematic chains are the same,they are isomorphic,otherwise they are not.The effectiveness of this method is proved by a large number of examples.Because of its simplicity,efficiency and convenience for com⁃puter execution,it can be considered as a new option for isomorphism screening.