Mobility analysis of multi-configuration Rubik's Cube mechanism based on the reciprocal screws

Abstract This paper focuses on the establishment of the kinematic diagram and the mobility of Rubik's Cube. Owing to the complex and variable characteristics of Rubik's Cube mechanism, a method of separating the inner and outer loops of Rubik's Cube mechanism and analyzing the Rubik's Cube with 1/8 module as a unit is proposed. Based on the topological graph and adjacency matrix, the kinematic diagram of Rubik's Cube unit which is in the first octant in both aligned and non-aligned states is constructed. On this basis, an analytical method for mobility due to the characteristics of strong coupling between the loops is proposed which is to separate the constraint of the internal and external of the mechanism, to successively decompose the mechanism by layer, then to process the front and back basic loops in proper order. Besides, a method is proposed to classify the sub-pieces and to decompose the coupling loops according to the direction of motion and the directed graph. Based on the screw theory and the “modified K-G formula”, the mobility of Rubik's Cube is obtained when it is in aligned and non-aligned states. Further, the theoretical analysis results are verified by the ADAMS.