Analysis of structural composition and representation of topological structures of Rubik's Cube mechanism. (June 2019) - Zeng, Daxing; Li, Ming; Wang, Juanjuan; Sun, Shuiyu; Luo, Xueling; Hou, Yulei; Lu, Wenjuan; Huang, Zhen
Highlights: The multi-configuration features of Rubik's Cube mechanism are introduced. The relationship between the configurations and the characteristic dimensions is obtained. A method for describing the Rubik's Cube mechanism topological structure is proposed. Abstract: Rubik's Cube is popular in the world for its beautiful simple complexity. The ingenious Rubik's Cube mechanism, whose structure is different from traditional mechanisms, has been paid more attention to as a toy or mathematical content. However, little attention has been paid to the investigation of its mechanical structure. In this paper, multi-configuration feature of the classic 3 × 3 × 3 Rubik's Cube is first investigated systematically, aiming at establishing the composition theory system of the Rubik's Cube mechanism and laying the foundation for the development and application of such mechanism. Firstly, the structural composition of the mechanism is analyzed and two new concepts of kinematic pairs called combined planar pair and spherical pair are defined, based on which the relationship between the configurations and characteristic dimensions of Rubik's Cube are analyzed in a single-operation, and its mapping relationship and the configurations change law of the Rubik's Cube mechanism are obtained subsequently. The different topological structures of Rubik's Cube are presented using graph theory and a new description method using a customized adjacency matrix for describing Rubik's Cube topological structure is established. The research is helpful for guiding the topological structure design and analysis of the multi-structure mechanisms containing dimension information.