Similarity recognition and isomorphism identification of planar kinematic chains

et al. 2021

Chin. J. Mech. Eng.

Self Cite

Isomorphism detection is fundamental to the synthesis and innovative design of kinematic chains (KCs). The detection can be performed accurately by using the similarity of KCs. However, there are very few works on isomorphism detection based on the properties of similar vertices. In this paper, an ameliorated multi-order adjacent vertex assignment sequence (AMAVS) method is proposed to seek out similar vertices and identify the isomorphism of the planar KCs. First, the specific definition of AMAVS is described. Through the calculation of the AMAVS, the adjacent vertex value sequence reflecting the uniqueness of the topology features is established. Based on the value sequence, all possible similar vertices, corresponding relations, and isomorphism discrimination can be realized. By checking the topological graph of KCs with a different number of links, the effectiveness and efficiency of the proposed method are verified. Finally, the method is employed to implement the similar vertices and isomorphism detection of all the 9-link 2-DOF(degree of freedom) planar KCs.

Section: Initial Value and Amavsmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Similar Vertices and Isomorphism Detection for Planar Kinematic Chains Based on Ameliorated Multi-Order Adjacent Vertex Assignment Sequence

et al. 2021

Chin. J. Mech. Eng.

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“…In this subsection, the method in our previous work 22 is applied to renumber a graph if the DMSs of two graphs are the same. The identification graph is divided into reference and analogy graphs for convenience.…”

Section: Numbering Rulesmentioning

confidence: 99%

Topological invariant and definition method for detecting isomorphism in planar kinematic chains

Cui

Proceedings of the Institution of Mechanical Engineers, Part C:

et al. 2020

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Isomorphism identification is an essential step in mechanism configuration synthesis. Although various detection methods have been proposed, some of them can only effectively identify kinematic chains (KCs) within 10 links or complex programs that are needed to identify multilink KCs. In this study, a new isomorphism identification method is proposed based on the distance concept of graphs and the graph theory definition of isomorphism. In addition to two complex 21- and 28-link planar simple-joint KCs (PSKCs), the proposed algorithm is tested on the complete atlas of 8-link 1-DOF, 9-link 2-DOF, 10-link 1-DOF, 12-link 1-DOF, and 13-link 2-DOF PSKCs. The algorithm is also tested on 6-link 1-DOF and 7-link 1-DOF planetary gear trains (PGTs) to detect isomorphism. All results are in agreement with those of the existing literature. The method is fully automated via a computer program and has been verified to be reliable and efficient.

“…The innovative design of mechanism structure is still the key step of product upgrading [1][2]. The correct solution of the similarity vertices [3] can not only reduce the number of isomorphism identification, but also provide a theoretical basis for the selection of rack, input and output components. In 1992, Yan [4] proposed a new mechanism design technology, called regenerative KCs method, which essentially represents the logical reasoning of the regeneration process of KCs.…”

Section: Introductionmentioning

confidence: 99%

Improved high-order adjacent vertex assignment sequence for similarity vertices and isomorphism identification of planar kinematic chains

et al. 2020

Preprint

Self Cite

Isomorphism identification is fundamental to synthesis and innovative design of kinematic chains (KCs). The identification can be performed accurately by using the similarity of KCs. However, there are very few researches on isomorphism identification based on the properties of similarity vertices. In this paper, an improved high-order adjacent vertex assignment (IHAVS) sequence method is proposed to seek out the similarity vertices and identify the isomorphism of the planar KCs. First, the specific definition of IHAVS is described. Through the calculation of the IHAVS, the adjacent point value sequence reflecting the uniqueness of the structural features is established. Based on the value sequence, all possible similarity vertices, corresponding relations and isomorphism discrimination can be realized. By checking the topological diagrams of KCs of different number of links, the correctness of the proposed method are verified. Finally, the method is used to find the similarity vertices of all the 9-link 2-DOF(degree of freedom) planar KCs.