A New Method to Detect Isomorphism in Kinematic Chains

Abstract

The present work deals with the problem of detection of isomorphism, which is frequently encountered in structural synthesis of kinematic chains (KC). A new method based on theoretic approach, easy to compute and reliable is suggested in this paper. The KC are represented in the form of the Joint-Joint [JJ] matrices. Two structural invariants derived from the characteristic polynomials of the [JJ] matrix of the KC are the sum of absolute characteristic polynomial coefficients (shortened as ΣJJ) and maximum absolute value of the characteristic polynomial coefficient (shortened as MJJ). These invariants are used as the composite identification number of a KC and mechanisms. It is capable of detecting isomorphism in all types of planar kinematic chains. This study will help the designer to select the best KC and mechanisms to perform the specified task and avoid duplication at the conceptual stage of design. The application this study is in research and development industries. The proposed method has been explained with the help of examples. The KC of 1-F, 8-links, and 10-links as well as 2-F, 9-link has been tested and the results are in complete agreement with the available literature of structural synthesis.