Abstract For mechanism design, the isomorphic kinematic chains (KCs) should be deleted to improve design efficiency. At present, most methods of isomorphism detection involve complex concepts and comparison of intermediate parameters. Moreover, when the number of components increases, it is complex and difficult to discriminate a large number of KCs in short time. However, the molecular topological index is proposed to identify isomer in organic chemistry, which shows excellent abilities for isomer recognition. In some respects, topological graph of kinematic chain is similar to chemical molecular model. Therefore, this idea is adopted to obtain extended adjacency identification index (EAID) which fits for isomorphism detection of KCs, namely KC-EAID. If two topological graphs have same KC-EAID value, then they are isomorphic. Otherwise, they are not. Three kinds of kinematic chains, including simple joints KCs, multiple joints KCs and gear-link KCs are given to verify effectiveness of this index in isomorphism detection. For KC-EAID index, it requires a few known quantities and no comparison of intermediate parameters. The algorithm only includes the calculation of matrices, which saves operation time. Therefore, KC-EAID can be used as a powerful tool for isomorphism detection in number synthesis of KCs.

中文翻译：

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一种基于拓扑索引的各种运动链同构检测新算法

摘要 在机构设计中，应删除同构运动链（KCs）以提高设计效率。目前，大多数同构检测方法都涉及复杂的概念和中间参数的比较。而且，当组件数量增加时，在短时间内区分大量的 KC 变得复杂且困难。然而，在有机化学中提出了分子拓扑指数来识别异构体，显示出优异的异构体识别能力。在某些方面，运动链的拓扑图类似于化学分子模型。因此，采用这一思想得到了适用于KCs同构检测的扩展邻接识别指数(EAID)，即KC-EAID。如果两个拓扑图具有相同的 KC-EAID 值，则它们是同构的。除此以外，他们不是。给出了三种运动链，包括简单关节KCs、多关节KCs和齿轮连杆KCs，以验证该指标在同构检测中的有效性。对于 KC-EAID 指数，它需要几个已知量，不需要比较中间参数。该算法只包括矩阵的计算，节省了运算时间。因此，KC-EAID 可以作为 KCs 数合成中同构检测的有力工具。