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research-article

AN INNOVATIVE APPROACH TO DETECT ISOMORPHISM IN PLANAR AND GEARED KINEMATIC CHAINS USING GRAPH THEORY

[+] Author and Article Information
Vinjamuri Venkata Kamesh

Associate Professor of Mechanical Engineering, Aditya Engineering College, SURAMPALEM-533 437, East Godavari District, Andhra Pradesh INDIA
kameshvv@gmail.com

Kuchibhotla Mallikarjuna Rao

Professor of Mechanical Engineering, University College of Engineering, JNTUK, KAKINADA-533 003, East Godavari District, Andhra Pradesh INDIA
rangaraokuchibhotla@gmail.com

Annambhotla Balaji Srinivasa Rao

Professor of Mechanical Engineering, Sri Vasavi Institute of Engineering and Technology, NANDAMURU-521369, Pedana Mandal, Krishna District, Andhra Pradesh INDIA
absrao71@gmail.com

1Corresponding author.

ASME doi:10.1115/1.4037628 History: Received February 07, 2017; Revised August 03, 2017

Abstract

Detection of isomorphism in planar and geared kinematic chains is an interesting area since many years. Enumeration of planar and geared kinematic chains becomes easy only when isomorphism problem is resolved effectively. Many researchers proposed algorithms based on topological characteristics or some coding which need lot of computations and comparisons. In this paper, a novel and simple algorithm is proposed based on graph theory by which elimination of isomorphic chains can be done very easily without any tedious calculations or comparisons. A new concept 'Net distance' is proposed based on the graph theory to be a quantitative measure to assess isomorphism in planar kinematic chains as well as geared kinematic chains. The proposed algorithm is applied on 9-link 2-degree of freedom (dof) distinct kinematic chains completely and results are presented in Appendix II. Algorithm is tested on examples from 8-link 1-dof, 10-link 1-dof, 12-link 1-dof and 15-link 4-dof planar kinematic chains (PKCs). The algorithm is also tested on 4, 6-link 1-dof geared kinematic chains (GKCs) to detect isomorphism. All the results are in agreement with the existing literature.

Copyright (c) 2017 by ASME
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