An Algorithm for Identifying the Isomorphism of Planar Multiple Joint and Gear Train Kinematic Chains

Zou, Yanhuo; He, Peng

doi:10.1155/2016/5310582

Cited by 7 publications

(2 citation statements)

References 30 publications

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“…The result is consistent with that by the algorithm based on the weighted-double-colour-contracted-graph (Zou and He 2016). Therefore, the proposed method in this paper is also applicable to kinematic chains with multiple joints.…”

Section: Discussionsupporting

confidence: 86%

A simple and efficient method for isomorphism identification of planar kinematic chains

Cai

Zhang

et al. 2021

Soft Comput

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Isomorphism identification plays an important role in structural design and innovative design.Based on the adjacency matrix and loop theory, a new method is proposed in this paper to identify the isomorphic kinematic chains. It enriches the application of loop-based theory for isomorphism identification. In the kinematic chain, links and joints are connected alternatively and every link corresponds to a fixed link degree. Due to the inherent characteristics, the labeled sequence of links can be random, which does not affect the result of isomorphism identification. By the programming software MATLAB, some examples with 6-, 8-, 10-, 11-, 12-link kinematic chains, and 15-vertex topological graphs are presented. Results show that the proposed method applies to topology graphs and kinematic chains with one or multiple joints. Compared with other methods, the proposed method is confirmed correctly. And there is no counterexample. It lays a solid foundation for structural synthesis in the future.

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Section: Discussionsupporting

confidence: 86%

A simple and efficient method for isomorphism identification of planar kinematic chains

Cai

Zhang

et al. 2021

Soft Comput

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show abstract

“…Consider a set of kinematic chains with multiple joints (Zou and He 2016). It is shown in Fig.…”

Section: Examplementioning

confidence: 99%

A simple and efficient method for isomorphism identification of planar kinematic chains

Cai

Zhang

et al. 2021

Preprint

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Isomorphism identification plays an important role in structural design and innovative design. Based on the adjacency matrix and loop theory, a new method is proposed in this paper to identify the isomorphic kinematic chains. It enriches the application of loop-based theory for isomorphism identification. In the kinematic chain, links and joints are connected alternatively and every link corresponds to a fixed link degree. Due to the inherent characteristics, the labeled sequence of links can be random, which does not affect the result of isomorphism identification. By the programming software MATLAB, some examples with 6-, 8-, 10-, 11-, 12-link kinematic chains, and 15-vertex topological graphs are presented. Results show that the proposed method applies to topology graphs and kinematic chains with one or multiple joints. Compared with other methods, the proposed method is confirmed correctly. And there is no counterexample. It lays a solid foundation for structural synthesis in the future.

show abstract

Detection of Isomorphism and Inversions of Kinematic Chains Using an Evolutionary Approach

Dewangan,

Prajapati

2024

Lecture Notes in Mechanical Engineering

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An Algorithm for Identifying the Isomorphism of Planar Multiple Joint and Gear Train Kinematic Chains

Cited by 7 publications

References 30 publications

A simple and efficient method for isomorphism identification of planar kinematic chains

A simple and efficient method for isomorphism identification of planar kinematic chains

A simple and efficient method for isomorphism identification of planar kinematic chains

Detection of Isomorphism and Inversions of Kinematic Chains Using an Evolutionary Approach

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