An efficient algorithm for distinct inversions and isomorphism detection in kinematic chains

Rizvi, Syed Shane Haider; Hasan, Ali; Khan, Rahmat Ali

doi:10.1016/j.pisc.2016.03.022

Cited by 17 publications

(3 citation statements)

References 10 publications

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“…chains with 9,10, 12 or even more number of links. The worth of this method is clear with the fact that the number of distinct mechanisms obtained for the eight link chains is 71 which is supported previous research of the author [11,12,13].…”

Section: Discussionsupporting

confidence: 81%

Categorization of Single Degree of Freedom Eight Link Kinematic Chains and Determination of Automorphism

Rizvi¹,

Kaleem²

2020

International Journal of Engineering Research and Technology

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Human civilization right from the stone age requires machines for their sustenance on the earth, the early age stone tools or the discovery of the wheel was the landmarks in the history of civilization but as the human race develops more and more complex machineries comes into existence and the basis of all these machines are the kinematic chains. The present study is to look into the available categorization of these kinematic chains in the literature and to develop a new and effective method of categorization of the available non-isomorphic single degree of freedom eight link chains and to find the automorphs present in each chain.

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Section: Discussionsupporting

confidence: 81%

Categorization of Single Degree of Freedom Eight Link Kinematic Chains and Determination of Automorphism

Rizvi¹,

Kaleem²

2020

International Journal of Engineering Research and Technology

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“…Various matrices are available in the literature like adjacency matrix, degree matrix, incidence matrix, joint-joint matrix etc. the author had also developed some matrices in his previous work chain identification matrix [15], link identity matrix [16], inversion adjacency matrix [17]. In this paper a modified form of chain identification matrix is used to determine isomorphism and automorphism in kinematic chains.…”

Section: Matrix Representation Of Kinematic Chainsmentioning

confidence: 99%

Isomorphism and Automorphism in Closed Kinematic Chains

Rizvi*

2019

IJEAT

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 Abstract: Effective mechanisms are the need of growing engineering world, the roots of which were found long back in the history of simple machines, but in today's scenario it changes the pace of development of any country by the use of robots, numeric control machines, automated transfer lines, space exploration programs defense systems etc. for this sound and effective mechanisms are required everywhere. Hence demand for the development new effective mechanisms increases day by day. At the starting phase in the designing of mechanisms structural requirements obtained from the functional requirements, but if there is some error in choosing the unique functional requirement to be converted into the structural requirement there may be a chance that the mechanism will not work or if it works it may be an isomer of some other kinematic chain in that situation it is a loss of effort, time of the designer and also the loss of money. The present work facilitates the designer to check the isomorphism and automorphism during the conceptual phase of designing the kinematic chain.

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“…Simoni et al (2009) applied the group theory technique to avoid the generation of isomorphic inversions and enumerated planar inversions with up to four independent loops. Dargar et al (2013) and Rizvi et al (2016) developed methods to determine structural invariants and identification numbers of kinematic chains to detect isomorphic kinematic chains inversions. Their methods were applied to synthesize kinematic chain inversions with up to 10 links.…”

Section: Introductionmentioning

confidence: 99%

Structural synthesis of plane kinematic chain inversions without detecting isomorphism

et al. 2021

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Abstract. A plane kinematic chain inversion refers to a plane kinematic chain with one link fixed (assigned as the ground link). In the creative design of mechanisms, it is important to select proper ground links. The structural synthesis of plane kinematic chain inversions is helpful for improving the efficiency of mechanism design. However, the existing structural synthesis methods involve isomorphism detection, which is cumbersome. This paper proposes a simple and efficient structural synthesis method for plane kinematic chain inversions without detecting isomorphism. The fifth power of the adjacency matrix is applied to recognize similar vertices, and non-isomorphic kinematic chain inversions are directly derived according to non-similar vertices. This method is used to automatically synthesize 6-link 1-degree-of-freedom (DOF), 8-link 1-DOF, 8-link 3-DOF, 9-link 2-DOF, 9-link 4-DOF, 10-link 1-DOF, 10-link 3-DOF and 10-link 5-DOF plane kinematic chain inversions. All the synthesis results are consistent with those reported in literature. Our method is also suitable for other kinds of kinematic chains.

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An efficient algorithm for distinct inversions and isomorphism detection in kinematic chains

Cited by 17 publications

References 10 publications

Categorization of Single Degree of Freedom Eight Link Kinematic Chains and Determination of Automorphism

Categorization of Single Degree of Freedom Eight Link Kinematic Chains and Determination of Automorphism

Isomorphism and Automorphism in Closed Kinematic Chains

Structural synthesis of plane kinematic chain inversions without detecting isomorphism

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