A new method to mechanism kinematic chain isomorphism identification

A New Concept to Detect Isomorphism in Kinematic Chains using Fuzzy Similarity Index

“…Quist and Soni give a loop method for kinematic chains [14]. A new method based on eigenvalues and eigenvectors of adjacent matrices of chains was also proposed [15]. The reliability of the existing spectral techniques for isomorphism detection was challenged by Sunkari, R.P., and Schmidt [16].…”

Derivation of valid contracted graphs from simpler contracted graphs for type synthesis of closed mechanisms

“…Refs. [13][14][15][16][17][18][19][20][21][22][23][27][28][29][30][31] mainly focus on the derivations of novel kinematic chains and their isomorphism identification with the consideration of the constraints and the poses of various kinematic chains using Lie group, group theory, screw theory and other approaches. Each of the above approaches has its merits and different focuses.…”

“…A vertex representing T, Q, P e and H is connected with 3, 4, 5 and 6 edges, respectively. A TG is similar to a CG, except that each of edges is composed of some B connected in series [12,31]. Let F be DoF of the mechanism, n k (k = 3, …, 6) be the numbers of (T, Q, P e , H) in TGs and CGs, respectively.…”

“…Kong, Gosselin [22,23], Wang [24] and Tarcisio [25] et al studied the topological synthesis and type synthesis of parallel mechanisms based on screw theory, a virtual joint, instantaneous kinematics and some wrist design requirements. Tuttle, Uicker, Shende, Rao, Yadav, Kong, Chang et al studied the identification of isomorphic kinematic chains Mechanism and Machine Theory 52 (2012) 206-218 [20,[26][27][28][29][30][31]. Lu et al derived many TGs with digit and TGs for planar 3-, 4-DOF mechanisms by distributing some binary links or digits over CGs using arrays and studied relative criteria [32,33].…”

Using characteristic strings to derive valid contracted graphs with hexagonal links plus other links for type synthesis of closed mechanisms

“…Uicker et al [16] studied the identification and recognition of equivalence of kinematic chains. Shende, Yadav, Kong, and Chang, Rao et al studied kinematic chain isomorphism identification [17][18][19][20][21]. Lu et al derived many TGs of planar 1, 2-DOF mechanisms using characteristic strings [22].…”