A novel algorithm for the isomorphism detection of various kinematic chains using topological index. (April 2020)

• Record Type: Journal Article
• Authors: Deng, Tao; Xu, Hui; Tang, Peng; Liu, Ping; Yan, Li
• Is Part Of: Mechanism and machine theory. Volume 146(2020)
• Publication Date: 2020-04
• Subjects: Isomorphism detection -- Extended adjacency trace -- Kinematic chains -- Simple joints -- Multiple joints; Machine theory -- Periodicals; Machinery -- Periodicals; Machines -- Périodiques; Génie mécanique -- Périodiques; Machine theory; Machinery; Periodicals; 621.81
• DOI: 10.1016/j.mechmachtheory.2019.103740
• Languages: English
• ISSNs: 0094-114X

Abstract

Highlights: A novel method using KC-EAID index is proposed for the isomorphism detection. Several specific terminologies of a topological graph are defined. The effectiveness of the index is verified by three kinds of kinematic chains. The algorithm is simple and convenient for computer program. 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.