Title: A new method for distinct inversions and isomorphism detection in kinematic chains

Authors: Syed Shane Haider Rizvi; Ali Hasan; Rasheed Ahmad Khan

Addresses: Mechanical Engineering Department, Jamia Millia Islamia (Central University), New Delhi 110025, India ' Mechanical Engineering Department, Jamia Millia Islamia (Central University), New Delhi 110025, India ' Mechanical Engineering Department, Galgotias University, Gautam Buddha Nagar, Greater Noida 201308, India

Abstract: In this paper, a new method for obtaining the number of distinct mechanisms from a kinematic chain based on a unique matrix representation of the links of a kinematic chain termed as link identity matrix (LI) is presented and a new invariant link signature (LS) is introduced, which is the sum of absolute value of the characteristics polynomial coefficient of the LI matrix for the representation of a distinct link. The similar values of the LS represent equivalent links further the LS values of a chain are used to determine the isomorphism among the kinematic chains and also assigns a signature to every chain known as chain signature (CS) obtained by summing all LS values of that chain and it is a unique identity assigned to every non-isomorphic chain.

Keywords: chain signature; distinct mechanisms; kinematic chains; link identity matrix; invariant link signature; distinct inversions; isomorphism detection.

DOI: 10.1504/IJMRS.2016.077039

International Journal of Mechanisms and Robotic Systems, 2016 Vol.3 No.1, pp.48 - 59

Received: 14 Nov 2015
Accepted: 17 Mar 2016
Published online: 18 Jun 2016 *

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