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In this paper a new, easy, reliable, and efficient method to detect isomorphism and a catalogue of fixed link with its corresponding equivalent links in the distinct mechanisms of kinematic chains of Group-A, has been presented. It is helpful to the new researchers and designers to choose the best mechanism to perform the desired task at the conceptual stage of design. The proposed method is presented by comparing the structural invariants ‘sum of the absolute values of the characteristic polynomial coefficients’ (SCPC) and ‘maximum absolute value of the characteristic polynomial coefficient’ (MCPC) of (JJ) matrices. These invariants are used to detect isomorphism in the mechanism kinematic chain having simple joints. The method is explained with the help of examples of planar kinematic chain.