A new matrix, called the joint-joint relation matrix, is defined for representing the structure of a kinematic chain. An algorithm has been developed for deriving the joint-joint distance matrix of a kinematic chain from its joint-joint relation matrix with the help of the computer. A new structural invariant, called the Arranged Sequence of Total Distance Ranks of all the Joints, and based on the concept of distance, has been developed for a kinematic chain, leading to the development of a simple methodology for detecting isomorphism among planar kinematic chains with simple joints.

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