A new algorithm of links labelling for the isomorphism detection of various kinematic chains using binary code

Isomorphism of kinematic chains (KCs) has always been a critical issue for the researchers dealing with structural synthesis. Consequently, many researchers of repute presented various methods during the last eight decades for the KCs with either simple and/or multiple joints. Binary code is one of such various methods, but the major problem lies in the algorithm of links labelling, which becomes cumbersome, in particular, for large KCs. The paper presents a simple algorithm of links labelling used to find out a binary sequence which, in turn, provides a maximum binary code (chain invariant). The algorithm is tested for six, seven, eight, nine, ten, eleven, twelve and fifteen links with simple joints, seven and eight links KCs with multiple joints and finally, the Epicyclic gear trains (EGTs) with four, five and six links for its efficiency and reliability. The results are in full agreement with the references taken for the purpose. The paper discusses, in a unique way, the decoding of the binary codes of different KCs also.