Application of link adjacency values to detect isomorphism among kinematic chains

Dargar, Ashok; Khan, Rahmat Ali; Hasan, Ali

doi:10.1007/s10999-010-9119-1

Cited by 22 publications

(8 citation statements)

References 14 publications

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“…The criteria for isomorphism (Xue et al, 2006;Dargar et al, 2010) is: if the relationship between points and edges of the two diagrams match each other, the two diagrams are isomorphic; if the rows or columns corresponding to the components with same properties in the adjacency matrices are equal after swapping transformation, the two diagrams are isomorphic.…”

Section: Remove the Isomorphic Mechanism Schemes Usingmentioning

confidence: 99%

Systematic synthesis method and prototyping of fixed-axle vehicular electrified mechanical transmission

Zhang

Zhong

Chen

2015

Int.J Automot. Technol.

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In the process of mechanism creative design, structure synthesis is the primary and the most important issue. This paper proposes a systematic and automatic synthesizing method of fixed-axle gear sets by means of morphological analysis. And the process is implemented to synthesize Electrified Mechanical Transmission (EMT) schemes which are parallel hybrid electric transmission composed of fixed-axle gear sets. First, independent design parameters as well as feasibility constraints and consistency conditions are defined by analyzing the structure and functions of EMT. According to these boundary conditions, structure variables such as the quantity of components and their connection relationship are solved. Then, the scheme quantity of each structure type is synthesized. Secondly, based on the abstraction of practical mechanisms with topology models, the corresponding adjacency matrixes are derived, and they are used to filtering unqualified schemes and retrieve all potential transmission paths of the remaining schemes. These potential transmission paths are further used to find out the layout and operating mode of each scheme. Finally, all schemes satisfying the structural and functional requirements are synthesized. For example, one EMT prototype is built based on one of the final schemes found and an ICE car is modified to adapt to such transmission. Vehicle test results verify the effectiveness and feasibility of the chosen transmission scheme.

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Section: Remove the Isomorphic Mechanism Schemes Usingmentioning

confidence: 99%

Systematic synthesis method and prototyping of fixed-axle vehicular electrified mechanical transmission

Zhang

Zhong

Chen

2015

Int.J Automot. Technol.

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“…Galán-Marín et al [15] first used the multi value neural network method to identify the isomorphism of KCs. In the same year, Dargar et al [16] proposed to identify isomorphism by comparing the first-order and second-order adjacent component values of the KCs, but Improved high-order adjacent vertex assignment sequence for similarity vertices and isomorphism identification of planar kinematic chains •3• this method has the defect that it can't describe the uniqueness of each vertex in the topological graph. Yang et al [17] proposed a method of detecting isomorphism based on the correlation matrix of KCs.…”

Section: Introductionmentioning

confidence: 99%

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

Sun

et al. 2020

Preprint

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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.

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“…Simultaneously, the structurally unique mechanisms can be obtained from the kinematic chain by fixing link one by one. There is a high possibility of duplicate kinematic chain generation, which requires testing of isomorphism [6]. The most inefficient technique in structural synthesis is the test of isomorphism.…”

Section: Introductionmentioning

confidence: 99%

A distinct matrix representation of the planar kinematic chains and isomorphism recognition

Alam¹,

Suhaib²

2019

JMES

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Structural synthesis of kinematic chains has been an indispensable area of the mechanismdesign problem. The duplication may occur while developing kinematic chains. Therefore, an isomorphic test is required to eliminate duplication. For this purpose, the numbers of methods are proposed during recent years. However, most of the methods are complex and difficult to understand, and fulfil the only primary condition, but not the secondary conditions for isomorphism detection. In the present work, a new method is introduced to detect isomorphism in planar kinematic chains (KCs) fulfilling both primary and secondary conditions. First, KC's are topologically transformed into skeleton diagrams, and then skeleton matrices [S] and identification strings [IS] are formulated consequently. In order to detect isomorphism, the IS is considered as an invariant string of a KC which in turn, enables the detection of isomorphism between the KCs. The proposed method accurately recognizes isomorphism up to 12 links KCs with no counter examples found in the literature. Three examples with one degree of freedom having 10 links 12 joints, 10 links 13 joints and 12 links three degree of freedom systems are introduced to reveal the reliability and strength of the proposed method.

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Application of link adjacency values to detect isomorphism among kinematic chains

Cited by 22 publications

References 14 publications

Systematic synthesis method and prototyping of fixed-axle vehicular electrified mechanical transmission

Systematic synthesis method and prototyping of fixed-axle vehicular electrified mechanical transmission

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

A distinct matrix representation of the planar kinematic chains and isomorphism recognition

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