Title: Joint resistance method for determination of isomorphism among planar kinematic chains and their derived mechanisms

Authors: Dharmendra Singh; Aas Mohammad; R.A. Khan

Addresses: Mech. Engg. Deptt., Ideal Institute of Technology Govindpuram, Ghaziabad, India ' Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi, India ' Mech. Engg. Deptt., Galgotia College of Engineering and Technology, Greater Noida, India

Abstract: The detection of isomorphism among kinematic chains and their derived mechanism has been a hot area of research for the last several years. In this paper a joint resistance method is proposed and it is tested for planar kinematic chains up to 12 links. In this method, the kinematic chains are represented in form of resistance graph and from that graph a Laplacian matrix is generated which is further transformed into an equivalent joint resistance matrix. The sums of the squares of resistances are used as an index for isomorphism identification among kinematic chains. This method is successfully examined for one degree of freedom, 6, 8, 10 links planar kinematic chains, 9 links two degree of freedom KC and 10 links three degree of freedom planar kinematic chains.

Keywords: distinct mechanisms; degrees of freedom; DOF; Laplacian matrix; joint resistance matrix; isomorphism identification; planar kinematic chains; resistance graph.

DOI: 10.1504/IJMRS.2015.069037

International Journal of Mechanisms and Robotic Systems, 2015 Vol.2 No.2, pp.182 - 194

Received: 29 Oct 2014
Accepted: 27 Jan 2015

Published online: 24 Apr 2015 *

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