Topology and Motion Diagram of the Third-order Cube Mechanism

The seemingly simple and compact Rubik's cube mechanism can actually realize the ever-changing movement, this wonderful model is beyond the traditional concept of mechanism and mechanism design method. The classical third-order cubic cube is taken as the research object, from the establishment of the motion diagram of the Rubik's cube mechanism as a breakthrough to explore the problem of mechanism in the world of Rubik's cube. The components and kinematic pairs in the Rubik's cube mechanism are analyzed, and two new kinematic pairs are defined to describe the problem of switching between movable and relatively fixed connections between components in the process of Rubik's cube movement. The aligned state and non-aligned state are defined to express the change of the configurations of the Rubik's cube mechanism in the process of rotation, the connection relationship between components in these two configurations is described by the mechanism topology diagram, and the adjacency matrix is used to reflect the location relationship and topological characteristics of components, so that the graphic expression of Rubik's cube mechanism can be transformed into mathematical expression. Then, in order to modularize the complex Rubik's cube mechanism, the method of dividing the internal and external constraints of the whole Rubik's cube and extracting the kinematic unit mechanism of the Rubik's cube is adopted, combining with the sub-adjacency matrix of the unit mechanism extracted from the corresponding configuration adjacency matrix of the Rubik's cube, taking the first octant unit mechanism as an example, the motion diagram of the external loop Rubik's cube mechanism in the aligned and non-aligned states are established respectively. The research work in this paper provides a reference for the structural analysis of non-traditional, variable topology, multi-configuration and multi-loop mechanisms, and provides a model for the follow-up analysis of freedom and motion characteristics of Rubik's cube mechanisms.