Topological structure of Rubik’s cube mechanism and synthesis of the regular hexahedron Rubik’s cube mechanism

This study investigates the factors affecting the topology of Rubik’s cube mechanism (RCM) and presents the synthesis theory of RCM. First, the revolute axis symmetry of the RCM is described and analyzed, and the general expression needed for the revolute axis to meet the symmetry is introduced. Next, the symmetry expression of the revolute pair contact surface (RPCS) of the RCM is given. The intersection between the RPCSs is analyzed via the adjacency matrix, and the adjacency matrix characteristics are given along with the motion characteristics of RCM. After determining the RPCS intersection, its topology is studied. Finally, the synthesis theory of RCM is presented, and the synthesis process and flowchart are proposed. The regular hexahedron RCMs with different topological structures are obtained after applying the synthesis theory. Hence, the theory proposed in this study provides strong theoretical support for the synthesis of other new RCMs.