Kinematic chains isomorphism identification using link connectivity number and entropy neglecting tolerance and clearance

It has always been a challenge for the researchers to detect isomorphism of the kinematic chains since this leads to the most critical and intolerable problem of duplicate structures. In order to avoid duplication among the kinematic chains, there has always been a need to develop an easy, reliable and efficient method. In the present paper, an attempt has been made by involving two new invariants i.e. power and efficiency (neglecting link tolerance and joint clearance) for detecting the isomorphism among the kinematic chains. The invariants are calculated on the basis of entropy, which refers to the average information concept taken from the information theory. The validity and reliability of this method is demonstrated with the help of several simple joints kinematic chains (taken from the references given) of single and multi-degree of freedom (dof) to verify the results. The proposed method is very simple and reliable in the identification of isomorphism and also provides a freedom to decode a particular link.