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.

中文翻译：

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基于往复螺杆的多配置魔方机构的运动性分析

摘要 本文重点研究了魔方运动学图的建立和移动性。针对魔方机制复杂多变的特点，提出了一种以1/8模块为单位，分离魔方机制内外循环，分析魔方的方法。基于拓扑图和邻接矩阵，构建了第一八分圆内的魔方单元在对齐和非对齐状态下的运动学图。在此基础上，针对回路之间强耦合的特点，提出了一种流动性分析方法，即分离机构内部和外部的约束，逐层分解机构，然后处理前、后处理。以正确的顺序返回基本循环。除了，提出了一种根据运动方向和有向图对子块进行分类和分解耦合回路的方法。基于螺旋理论和“修正KG公式”，得到了魔方在对齐和非对齐状态下的迁移率。此外，理论分析结果也得到了ADAMS的验证。