Topological symmetry identification of kinematic chains based on topological index

Deng, Tao; Xu, Hui; Wu, Changjun; Zhang, Lu; Gan, Zhihan

doi:10.1016/j.mechmachtheory.2020.104099

Cited by 6 publications

(7 citation statements)

References 35 publications

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“…Our conclusion can be verified by Ref. [28], whereas the method in Ref. [29] fails to correctly detect symmetric vertices in these two kinematic chains.…”

Section: Synthesis Of Multiple Joint Kinematic Chainssupporting

confidence: 64%

“…Yang et al [27] developed a perimeter loop-based method to determine nonsymmetric links and synthesize nonisomorphic kinematic chain inversions with complex topology. Based on the link adjacency relationship, Deng et al [28] developed the extended adjacency identification index to recognize symmetric links and joints of various kinds of kinematic chains. Sun and his coworkers [29][30][31] presented a method based on the power of adjacency matrix to detect symmetric links and joints.…”

Section: Introductionmentioning

confidence: 99%

“…However, many existing methods cannot guarantee reliability because they fail in some cases, as discussed in Refs. [27,28]. On the other hand, most studies only focused on the kinematic chains with simple joints, whereas other types of kinematic chains, such as those chains containing multiple joints, prismatic pairs, and geared pairs, were rarely discussed.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Symmetry Detection and Topological Synthesis of Mechanisms of Powertrains

Yang¹,

Li²

2022

Energies

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The function of vehicle powertrains (including hybrid powertrains) is to transmit power from the power source (engine or electric machine) to driving wheels. The planetary gear train (PGT) is a core structure of mechanisms of powertrains. The detection of topological symmetry is helpful for improving the efficiency of mechanism design. In this paper, we present a fully automatic and reliable method for detecting symmetry of plane kinematic chains and extend this method to symmetry detection and the topological design of mechanisms of powertrains. First, the topological model and adjacency matrix are introduced to represent various kinds of plane kinematic chains. Then, the moment matrix of the kinematic chain is established to obtain link groups, based on which we propose an algorithm to generate the unique numerical code of each link and precisely detect the symmetry. Our method is applied to synthesize different kinds of plane kinematic chains and mechanisms, which can improve the design efficiency of mechanisms of powertrains and other mechanical devices.

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“…Our conclusion can be verified by Ref. [28], whereas the method in Ref. [29] fails to correctly detect symmetric vertices in these two kinematic chains.…”

Section: Synthesis Of Multiple Joint Kinematic Chainssupporting

confidence: 64%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Symmetry Detection and Topological Synthesis of Mechanisms of Powertrains

Yang¹,

Li²

2022

Energies

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“…The structure synthesis [1][2][3] of KC is a difficult problem and research hot spot in mechanism innovative design. Some problems such as the generation method of KC [4,5],rigid sub chain elimination [6,7], isomorphism identification [8][9][10], auto-sketching of topological and structural graphs [11,12] and so on, must be solved in the process of structure synthesis of KC.…”

Section: Introductionmentioning

confidence: 99%

A new Isomorphism Identification Method for Kinematic Chain Based on Exchange and Compare of Lower-Triangle Matrix with Whole Information

Sun

Liu

et al. 2023

Preprint

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Isomorphism identification is an important step and costs major counting labor (more than 90%) in kinematic chain (KC) structure synthesis, many isomorphism identification methods have been proposed by researchers in past decades. The identification principle is simple and easy to be understood, the result has no objection, and the programming is simple and efficient, these are main criterions for isomorphism identification method. A new Matrix with Whole Information (MWI) has been proposed to describe the structure information of KC, and the principles of determining multiple joints and polygonal links are also proposed. Based on the principle that the Lower Triangular Matrix with Whole Information (LTMWI) can uniquely express the structure of KC, a new isomorphism identification method, based on the exchange and compare of LTMWI is proposed. This method is based on the law of exchange of links’ numbers and key points’ numbers, and two KCs are expressed by LTMWI, in which one LTMWI is selected as the datum matrix, the key points are arranged in different groups and non-zero elements of key points are moved forward, the definite and indefinite key points are obtained, under the assumption that all key points in the same positions have the mapping relationships one-to-one between exchange matrix and datum matrix, a finite number of exchange matrices are generated and compared with datum matrix, then isomorphism can be drawn. This method has the advantages such as simple principle, easy to program and only analysis and comparisons are needed in the identification process. The isomorphism identification results and the mapping relationships of links and even revolute pairs can all be obtained. The isomorphic analysis results of several KCs have shown the above characteristics of this method.

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“…The role of symmetry in mechanical design is mainly reflected in meeting the requirements. For example, the symmetry idea is used to reduce the calculation time or modeling difficulties [8][9][10][11][12]. Some scattered studies on mechanical symmetry believe that symmetry is one of the optimization criteria [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Association Analysis between Mechanical Symmetry and Requirements

2022

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This paper focuses on obtaining the association rules between the symmetry of different mechanical structure layers and requirements through data mining, then suggests the selection of symmetry schemes under different requirement conditions, based on the mined association rules and their strength. Firstly, a thousand symmetry structure cases, namely text data, are transformed into binary data. Then, the data analysis software RapidMiner is used to build an association rule mining model to obtain the association rules from symmetry to symmetry, from symmetry to requirements, from requirements to requirements and from requirements to symmetry. Among them, this paper focuses on the association rules with requirements as the premise and symmetry as the conclusion. Finally, according to the support and confidence of the association rules, the selection of symmetry under a single requirement, multiple requirements and decomposable requirements is discussed and summarized.

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Topological symmetry identification of kinematic chains based on topological index

Cited by 6 publications

References 35 publications

Symmetry Detection and Topological Synthesis of Mechanisms of Powertrains

Symmetry Detection and Topological Synthesis of Mechanisms of Powertrains

A new Isomorphism Identification Method for Kinematic Chain Based on Exchange and Compare of Lower-Triangle Matrix with Whole Information

Association Analysis between Mechanical Symmetry and Requirements

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