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Abstract

Isomorphism identification is an essential step in mechanism configuration synthesis. Although various detection methods have been proposed, some of them can only effectively identify kinematic chains (KCs) within 10 links or complex programs that are needed to identify multilink KCs. In this study, a new isomorphism identification method is proposed based on the distance concept of graphs and the graph theory definition of isomorphism. In addition to two complex 21- and 28-link planar simple-joint KCs (PSKCs), the proposed algorithm is tested on the complete atlas of 8-link 1-DOF, 9-link 2-DOF, 10-link 1-DOF, 12-link 1-DOF, and 13-link 2-DOF PSKCs. The algorithm is also tested on 6-link 1-DOF and 7-link 1-DOF planetary gear trains (PGTs) to detect isomorphism. All results are in agreement with those of the existing literature. The method is fully automated via a computer program and has been verified to be reliable and efficient.

Keywords

Isomorphism identification kinematic chains structural synthesis distance matrix planetary gear trains

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References

Tsai

L-W.

Mechanism design: Enumeration of kinematic structures according to function. Boca Raton: CRC Press, 2000.

Uicker

Jr and Raicu

A method for the identification and recognition of equivalence of kinematic chains. Mech Mach Theory 1975; 10: 375–383.

Mruthyunjaya

Balasubramanian

In quest of a reliable and efficient computational test for detection of isomorphism in kinematic chains. Mech Mach Theory 1987; 22: 131–139.

Yan

H-S

Hwang

W-M.

A method for the identification of planar linkage chains. J Mech Transm Autom Des 1983; 105: 658–662.

Dube

Rao

New characteristic polynomial-a reliable index to detect isomorphism between kinematic chains. J Indian Inst Sci 2013; 66: 227.

Sunkari

Schmidt

LC.

Reliability and efficiency of the existing spectral methods for isomorphism detection. J Mech Des 2006; 128: 1246–1252.

Rao

Kinematic chains-isomorphism, inversions and type of freedom using the concept of hamming distances. Indian J Technol 1988; 26: 105–109.

Rao

Hamming number technique – II. Generation of planar kinematic chains. Mech Mach Theory 1997; 32: 489–499.

Rao

Raju

DV.

Application of the hamming number technique to detect isomorphism among kinematic chains and inversions. Mech Mach Theory 1991; 26: 55–75.

10.

Dharanipragada

Chintada

Split hamming string as an isomorphism test for one degree-of-freedom planar simple-jointed kinematic chains containing sliders. J Mech Des 2016; 138: 082301.

11.

Sun

Kong

Sun

The improved hamming number method to detect isomorphism for kinematic chain with multiple joints. J Adv Mech Des Syst Manuf 2017; 11: JAMDSM0061–JAMDSM0061.

12.

Mruthyunjaya

Kinematic structure of mechanisms revisited. Mech Mach Theory 2003; 38: 279–320.

13.

Ambekar

Agrawal

Canonical numbering of kinematic chains and isomorphism problem: Min code. Mech Mach Theory 1987; 22: 453–461.

14.

Fang

Freudenstein

The stratified representation of mechanisms. Journal of Mechanical Design 1990; 112: 514–519.

15.

Shin

Krishnamurty

Development of a standard code for colored graphs and its application to kinematic chains. Journal of Mechanical Design 1994; 116: 189–196.

16.

Rai

RK.

A new algorithm of links labelling for the isomorphism detection of various kinematic chains using binary code. Mech Mach Theory 2019; 131: 1–32.

17.

Rai

Punjabi

Kinematic chains isomorphism identification using link connectivity number and entropy neglecting tolerance and clearance. Mech Mach Theory 2018; 123: 40–65.

18.

Yadav

Pratap

Agrawal

Computer aided detection of isomorphism among binary chains using the Link-Link multiplicity distance concept. Mech Mach Theory 1996; 31: 873–877.

19.

Kamesh

Rao

ABS.

An innovative approach to detect isomorphism in planar and geared kinematic chains using graph theory. J Mech Des 2017; 139: 122301.

20.

Ding

Huang

Isomorphism identification of graphs: Especially for the graphs of kinematic chains. Mech Mach Theory 2009; 44: 122–139.

21.

Zeng

Fan

Dong

, et al. A fast algorithm for kinematic chain isomorphism identification based on dividing and matching vertices. Mech Mach Theory 2014; 72: 25–38.

22.

Sun

Cui

, et al. Similarity recognition and isomorphism identification of planar kinematic chains. Mech Mach Theory 2020; 145: 103678.

23.

Yang

Ding

The complete set of one-degree-of-freedom planetary gear trains with up to nine links. J Mech Des 2019; 141: 043301.

24.

Yang

Ding

, et al. New graph representation for planetary gear trains. J Mech Des 2018; 140: 012303.

25.

Ding

Huang

Yang

, et al. Automatic generation of the complete set of planar kinematic chains with up to six independent loops and up to 19 links. Mech Mach Theory 2016; 96: 75–93.

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Topological invariant and definition method for detecting isomorphism in planar kinematic chains

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