A Method to Detect Isomorphism in Planar Kinematic Chains

For synthesizing kinematic chains of a given number of links and degree of freedom, detection of isomorphism is essential. Two kinematic chains are called isomorphic if they have equivalent topological configuration. The exertion for detection of isomorphism among planar kinematic chains is being researched for a long time to avoid redundancy. In the past, researchers have used several methods like characteristic polynomial-based approaches, Hamming number method, path and distance-based techniques, and many more complex algorithms to detect isomorphism. In this work, an index for detection of isomorphism among planar kinematic chains is proposed by considering the distance matrix and degree of links matrix. Kinematic chains are isomorphic, if they have same index else they are non-isomorphic. Hence, to detect isomorphism among different kinematic chains, the proposed technique is implemented successfully for 8-link single degree of freedom and 9-link double degree of freedom kinematic chains.