Derivation and isomorphism identification of valid topological graphs for 1-, 2-DOF planar closed mechanisms by characteristic strings

Abstract

A characteristic string approach is presented for derivation and isomorphism identification of valid topological graphs (TGs) for some 1, 2-DOF (degree of freedom) planar closed mechanisms from the contracted graphs (CGs). First, topological graph (TG) is simplified by the topology graph with digits (DTG) for the 1-, 2-DOF planar closed mechanisms. Second, the equivalent conditions between the characteristic string and DTG are determined and verified by some created simulation mechanisms of valid TGs, a complicated derivation of TG is transformed into an easy derivation of the characteristic string. Third, the valid characteristic strings are derived corresponding to non-isomorphic TGs, and the invalid characteristic strings corresponding to the isomorphic and invalid TGs are determined using the characteristic string. Finally, many valid characteristic strings for the 2-DOF planar mechanisms are derived from some valid characteristic strings for the 1-DOF planar mechanisms.

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

“…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]. Each of the above approaches has its merits and different focus.…”