Automatic topological structural synthesis algorithm of planar simple joint kinematic chains

Zou, Yanhuo; He, Peng; Pei, Y. L.

doi:10.1177/1687814016638055

Cited by 14 publications

(8 citation statements)

References 29 publications

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“…It was a research hotspot in mechanism since the 1960s, with the development, several isomorphism identification methods were proposed by mechanism scholars. 1–10…”

Section: Introductionmentioning

confidence: 99%

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An isomorphism identification method of kinematic chain based on optimal arrangement and comparison of branch-chain matrix derived from dendrogram graph

Sun

Liu

et al. 2022

Advances in Mechanical Engineering

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Isomorphism identification is an essential step in the structure synthesis of Kinematic Chain (KC), and needs a large amount of analysis and calculation. To find an isomorphism identification method with simple rules, scientific feasibility and less analysis and calculation has always been a research hotspot of mechanism scholars. In this paper, the structure information of KC is described by dendrogram structure graph with multiple joints, and Branch-chain Matrix (BM) is separated from the dendrogram structure. The characteristics of BM are analyzed, and the concepts of intimacy between branch-chains and Repeatability Matrix (RM) corresponding to BM are proposed. Based on fact that both dendrogram graph and BM can uniquely determine the structural information of one KC, a new isomorphism identification method for KC, based on row optimal rearrangement and comparison of BM, is proposed. The operation steps are discussed in detail, and several cases are analyzed to show this method has advantages such as easy rules, small calculation of retrieval and comparison, and easy to be programmed.

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“…It was a research hotspot in mechanism since the 1960s, with the development, several isomorphism identification methods were proposed by mechanism scholars. 1–10…”

Section: Introductionmentioning

confidence: 99%

“…It was a research hotspot in mechanism since the 1960s, with the development, several isomorphism identification methods were proposed by mechanism scholars. [1][2][3][4][5][6][7][8][9][10] The existing isomorphism identification methods can be roughly divided into the following categories.…”

Section: Introductionmentioning

confidence: 99%

An isomorphism identification method of kinematic chain based on optimal arrangement and comparison of branch-chain matrix derived from dendrogram graph

Sun

Liu

et al. 2022

Advances in Mechanical Engineering

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“…In graph-based synthesis, the graph theory is used to represent a product and define the relationships between its components, and the graph concepts and theorems are employed to generate design candidates [23]. For now, graph-based synthesis approaches have been widely used in the synthesis, analysis and optimization process of linkage systems [24][25][26] and epicyclic gear trains [27,28]. Moreover, Bin proposed a computational conceptual design synthesis model based on space matrix [29], and he also integrated the functional synthesis of mechanisms with mechanical efficiency and cost to find out the optimal solution [30,31].…”

Section: Introductionmentioning

confidence: 99%

A Computational Synthesis Approach of Mechanical Conceptual Design Based on Graph Theory and Polynomial Operation

Han

Yang

et al. 2020

Chin. J. Mech. Eng.

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The design synthesis is the key issue in the mechanical conceptual design to generate the design candidates that meet the design requirements. This paper devotes to propose a novel and computable synthesis approach of mechanisms based on graph theory and polynomial operation. The graph framework of the synthesis approach is built firstly, and it involves: (1) the kinematic function units extracted from mechanisms; (2) the kinematic link graph that transforms the synthesis problem from mechanical domain into graph domain; (3) two graph representations, i.e., walk representation and path representation, of design candidates; (4) a weighted matrix theorem that transforms the synthesis process into polynomial operation. Then, the formulas and algorithm to the polynomial operation are presented. Based on them, the computational flowchart to the synthesis approach is summarized. A design example is used to validate and illustrate the synthesis approach in detail. The proposed synthesis approach is not only supportive to enumerate the design candidates to the conceptual design of a mechanical system exhaustively and automatically, but also helpful to make that enumeration process computable.

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“…15 Through these graphs, the mapping relationship between graph and structure was provided, and basic motion units were divided according to planets and so on. Sohn and Freudenstein, 16 Vucinan and Freudenstein, 17 and Zou et al 18 all made great progresses according to the theory. However, they still lack the complete expression of structure and properties of components.…”

Section: Introductionmentioning

confidence: 99%

The multi-attribute topological graph method and its application on power flow analysis in closed planetary gear trains

Cui

Gao

et al. 2018

Advances in Mechanical Engineering

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The concept of multi-attribute topological graph is proposed in this article to represent the characteristics of both structure and state for typical one-degree-of-freedom planar spur closed planetary gear trains. This method is well applied in power flow analysis and provides a graphical view for the types, values, directions, and transmission relationship of power flow, especially for the recirculation power representation. Furthermore, a template model of multi-attribute topological graph for closed planetary gear trains is also presented, which would be helpful to the multi-attribute topological graph generation for some certain types of closed planetary gear trains just by changing symbols in the template model. A corresponding software is also developed to make the analysis process more convenient. By inputting different parameters, the different visual results can be obtained automatically, thus benefiting engineers in conceptual design.

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Automatic topological structural synthesis algorithm of planar simple joint kinematic chains

Cited by 14 publications

References 29 publications

An isomorphism identification method of kinematic chain based on optimal arrangement and comparison of branch-chain matrix derived from dendrogram graph

An isomorphism identification method of kinematic chain based on optimal arrangement and comparison of branch-chain matrix derived from dendrogram graph

A Computational Synthesis Approach of Mechanical Conceptual Design Based on Graph Theory and Polynomial Operation

The multi-attribute topological graph method and its application on power flow analysis in closed planetary gear trains

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