Abstract
The topology graph is an effective tool for creating various complex mechanisms and machines. However, the derivation and the isomorphism identification of the topology graphs are quite complicated because topology graphs may include (binary, ternary,...) links. A digit topology circle Cj(k)i excluding (binary, ternary) links is proposed and studied for simplifying the derivation and isomorphism identification of the topology graph. First, the conceptions of Cj(k)i are explained and their derivations are studied. Second, a method of the character strings is proposed and studied for representing Cj(k)i and reducing the isomorphism Cj(k)i, and many different Cj(k)i are represented by different digit lines and digit arcs based on the proposed method, and many different Cj(k)i are constructed. Third, a rule for identifying isomorphism Cj(k)i is discovered and proved using the connections in the digit topology circle, and some isomorphism Cj(k)i are identified from constructed different Cj(k)i. Furth, many new different Cj(k)i with the ternary link are derived by adding ternary link into Cj(k)i. Finally, a closed mechanism of 6-DOF the hybrid machine tool/hybrid grasper is created by combining 37 binary links with the new digit topology circle C3(2)10 + ternary link; two closed mechanisms of the 6-DOF leg-foot are created by combining 46 binary links with digit topology circles C26(1)i (i = 101,104), respectively.