A computerized loop based approach for identification of isomorphism and type of mobility in planar kinematic chains

Some new invariants like chain string, link identification string, loop participation of joint frequency string and loop size frequency string of simple jointed kinematic chains are presented. The first step of the proposed method is to identify all possible loops of a kinematic chain and then these new invariants are developed. A modified loop-joint approach is proposed in this work as compared to the previous work in literature where loop-link matrix is formulated to search all the loops present in a kinematic chain. A computer program has been developed for formulating loop-joint matrix of kinematic chain and its all invariants. This method takes into consideration all the loops present, associated joints and links and is able to test isomorphism among kinematic chains and their inversions and also to detect type of mobility of multi degree of freedom kinematic chains. The proposed method is successfully tested for all kinematic chains upto five independent loops having any number of degree of freedom and no counter example is found. The detailed results of 9-link, M = 2 (mobility) and 10 link, M = 3 kinematic chains are provided with five types of mobility and results are in accordance with the results published in literature. The method is also explained with the help of some complex examples and presented in this paper.