Study of isomorphism in kinematic chains and mechanisms

The aim of this paper is to suggest a new and easy procedure that can be used to determine the isomorphism in kinematic chains and mechanisms. The procedure is based on theoretic approach of simple Linear Algebra theorem ‘Two similar square symmetric matrices have the same characteristic polynomials’. Here a new square joint-joint [JJ] matrix is suggested whose elements are either 0 or the degrees (type) of the link. Two structural invariants namely ‘sum of the absolute values of the characteristic polynomial coefficients’ [SCPC] and ‘maximum absolute value of the characteristic polynomial coefficient’ [MCPC] of [JJ] matrices are used for mapping the kinematic chains and mechanisms. The procedure is clarified with the aid of examples. The paper is extremely useful for research scholars and designers at the conceptual stage of engineering design