Representation of planar kinematic chains with multiple joints based on a modified graph and isomorphism identification
Representation of planar kinematic chains with multiple joints based on a modified graph and isomorphism identification
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DOI：
10.1016/j.mechmachtheory.2022.104793
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发表时间：
2022-06
影响因子：
5.2
通讯作者：
Kaijie Dong;Duanling Li;X. Kong
中科院分区：
文献类型：
--
作者：
Kaijie Dong;Duanling Li;X. Kong
多关节运动链的表示和同构识别是机构研究中亟待解决的关键问题。本文提出了一种改进的图--平面面图(PF图)。作为一个关键概念，面子被用来表示单一的、特定的关系是由多个事件组成的情况。文中还详细介绍了与PF图有关的其他一些基本概念。用PF图表示具有多个结点的KCs，反映了KCs的唯一性，实现了KCs与邻接矩阵和关联矩阵的一一对应。它还与其他表示KCs的方法建立了联系，并被证明适用于复杂的机械系统。给出了同构的充要条件，分析了置换相似的两个性质。在此基础上，提出了改进的特征值特征向量法和最大路径法，并将它们结合在一起形成了一种新的算法。此外，还证明了该算法的可靠性和有效性。
The representation and isomorphism identification of kinematic chains (KCs) with multiple joints are crucial issues to be solved in mechanism research. In this paper, a modified graph—planar face graph (PF graph), is proposed. As a key concept, “face” has been put forward to represent the case that a single, specific relationship is incident with multiple incidents. Some other basic concepts relating to PF graph are also explained in detail. PF graph is used to represent KCs with multiple joints and it reflects the uniqueness of KCs and realizes the one-to-one correspondence between KCs and adjacency and incident matrices. It also establishes relationships with other methods for representing KCs and it is proved to be suitable for complex mechanical systems. Moreover, the sufficient and necessary condition of isomorphism are derived, and two properties of permutation similarity are analysed. Based on them, the modified eigenvalue eigenvector method and the maximum path method are proposed, and they are integrated to form a new algorithm. In addition, the reliability and efficiency of the algorithm are proved.