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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.

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