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Supervised by Ministry of Industry and Information Technology of The People''s Republic of China Sponsored by Harbin Institute of Technology Editor-in-chief Yu Zhou ISSNISSN 1005-9113 CNCN 23-1378/T

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Related citation:Yulei Hou,Ting Zhou,Guoxing Zhang,Ming Li,Daxing Zeng.Topological Configuration and Rotation Analysis of the Three Order Rubik's Cube[J].Journal of Harbin Institute Of Technology(New Series),2020,27(5):49-58.DOI:10.11916/j.issn.1005-9113.2019014.
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Topological Configuration and Rotation Analysis of the Three Order Rubik's Cube
Author NameAffiliation
Yulei Hou School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, Hebei, China
Heavy-duty IntelligentManufacturing Equipment Innovation Center of Hebei Province, Yanshan University, Qinhuangdao 066004, Hebei, China 
Ting Zhou School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, Hebei, China 
Guoxing Zhang School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, Hebei, China 
Ming Li School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, Hebei, China 
Daxing Zeng School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, Hebei, China
Heavy-duty IntelligentManufacturing Equipment Innovation Center of Hebei Province, Yanshan University, Qinhuangdao 066004, Hebei, China 
Abstract:
The mechanism of three-order Rubik's Cube (RC) has the characteristics of recombination and variable degree of freedom, and it is difficult to accurately describe the degree of its freedom. This paper takes RC as the research object, and the adjacency matrix is constructed based on topology and graph theory in order to describe the variation rule of topological configuration in the single layer rotation of RC. In this paper, the degree of freedom of the RC in any shape can be described by defining the concept of entanglement degree of freedom, establishing a set of adjacency matrix, and determining the degree of freedom of the RC which is attributed to the number of non-zero elements in the set of adjacent matrix. The prime number is proposed to describe the rotation of the RC combined with the rotation recognition of RC, which is simple and convenient for computer processing. The research contents in this paper are beneficial to the study of RC from the perspective of mechanism science. Meanwhile, it is of great significance to the study of other complex mechanisms with variable degrees of freedom.
Key words:  mechanism of Rubik's Cube  topological configuration  adjacency matrix  degree of freedom  prime number
DOI:10.11916/j.issn.1005-9113.2019014
CLC NUMBER:TH122
Fund:
Descriptions in Chinese:
  

三阶魔方拓扑结构与旋转分析

侯雨雷12 ,周挺1 ,张国兴1 ,李明1 ,曾达幸12

(1. 燕山大学 机械工程学院,河北 秦皇岛 066004;2. 河北省重型智能制造装备技术创新中心,河北 秦皇岛 066004)

摘要:

三阶正方体魔方机构具有可重组、变自由度等特点,对其自由度的准确描述是研究的难点。本文以三阶正方体魔方为研究对象,基于拓扑学和图论的方法构建邻接矩阵,描述魔方单层转动过程中拓扑构态的变化规律。定义纠缠自由度的概念,建立邻接矩阵的集合,将魔方自由度的确定归结于寻找邻接矩阵集合中非零元素的数目,从而对魔方在任意状态下的自由度予以描述。结合魔方的转动识别,提出使用素数描述魔方转动的方法,计算简单,便于计算机处理。本文研究工作是对魔方从机构学角度研究的有益探索,对于其它变自由度复杂机构的研究具有借鉴意义。

关键词:魔方机构;拓扑;邻接矩阵;自由度;素数

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