Rubik’s Cube is a widely popular mechanical puzzle that has attracted attention around the world because of its unique characteristics. As a classic brain-training toy well known to the public, Rubik’s Cube was used...Rubik’s Cube is a widely popular mechanical puzzle that has attracted attention around the world because of its unique characteristics. As a classic brain-training toy well known to the public, Rubik’s Cube was used for scientific research and technology development by many scholars. This paper provides a basic understanding of the Rubik’s Cube and shows its mechanical art from the aspects of origin and development, characteristics, research status and especially its mechanical engineering design, as well as making a vision for the application in mechanism. First, the invention and origin of Rubik’s Cube are presented, and then the special characteristics of the cube itself are analyzed.After that, the present researches of Rubik’s Cube are reviewed in various disciplines at home and abroad, including the researches of Rubik’s Cube scientific metaphors, reduction algorithms, characteristic applications, and mechanism issues. Finally, the applications and prospects of Rubik’s Cube in the field of mechanism are discussed.展开更多
The mechanism of three⁃order Rubiks 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 mechanism of three⁃order Rubiks 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.展开更多
As part of the 4th industrial revolution,programmable mechanical metamaterials exhibit great application potential in flexible robotics,vibration control,and impact protection.However,maintaining a programmed state wi...As part of the 4th industrial revolution,programmable mechanical metamaterials exhibit great application potential in flexible robotics,vibration control,and impact protection.However,maintaining a programmed state without sustaining the external stimulus is often challenging and leads to additional energy consumption.Inspired by Rubik’s cube,we design and study an in-situ programmable and distribution-reconfigurable mechanical metamaterial(IPDR-MM).A matrix model is developed to model IPDR-MMs and describe their morphological transitions.Based on this model,the reinforcement learning method is employed to find the pathways for morphological transitions.We find that IPDR-MMs have controllable stiffness across several orders of magnitude and a wide range of adjustable anisotropies through morphology transformation.Additionally,because of the independence of the directions of morphology transformation and bearing,IPDR-MMs exhibit good stability in bearing and can readily achieve high stiffness.The Rubik’s cube-inspired design concept is also instructive for other deformable structures and metamaterials,and the current version of the proposal should be sufficiently illustrative to attract and broaden interdisciplinary interests.展开更多
在明确耕地细碎化(cultivated land fragmentation,CLF)会造成的消极和积极影响基础上,构建CLF评价体系,探索以因地制宜为理念差异化解决CLF现象的方法。以陕西省2020年耕地利用现状为例,从耕地的自然资源禀赋、空间聚集程度、利用便利...在明确耕地细碎化(cultivated land fragmentation,CLF)会造成的消极和积极影响基础上,构建CLF评价体系,探索以因地制宜为理念差异化解决CLF现象的方法。以陕西省2020年耕地利用现状为例,从耕地的自然资源禀赋、空间聚集程度、利用便利程度三个方面构建陕西省CLF程度三维魔方模型,对其CLF空间分异特征进行探索,并提出了改善CLF的策略。结果表明:陕西省CLF指数(CLFI)总体上呈现中间低、南北高的空间特征,CLFI最大值为0.796,最小值为0.020,均值为0.217,高值集中在陕南和关中交界的秦巴山区以及陕北东部地区。基于CLF特征和农业种植多样性、地区经济水平等影响因素以及耕地资源3个属性特征,提出了针对陕西省CLF的优化分区规划,其中包括保持提升区、集约归并区、设施优化区、资源改造区、综合提升区、综合整治区6类乡镇级引导分区,及以地区社会经济指标为基础划分的政策倾向区、加强整治区、资源倾向区、资源适配区4类县级引导分区,并结合两类分区结果的特征提出了不同地区土地整治的主要方向及关键问题。展开更多
基金Supported by National Natural Science Foundation of China(Grant No.51775473)Hebei Provincial Natural Science Foundation of China(Grant No.E2018203140)Hebei Provincial System Construction Project of Guide Program for Technology Innovation(Grant No.18241905D)
文摘Rubik’s Cube is a widely popular mechanical puzzle that has attracted attention around the world because of its unique characteristics. As a classic brain-training toy well known to the public, Rubik’s Cube was used for scientific research and technology development by many scholars. This paper provides a basic understanding of the Rubik’s Cube and shows its mechanical art from the aspects of origin and development, characteristics, research status and especially its mechanical engineering design, as well as making a vision for the application in mechanism. First, the invention and origin of Rubik’s Cube are presented, and then the special characteristics of the cube itself are analyzed.After that, the present researches of Rubik’s Cube are reviewed in various disciplines at home and abroad, including the researches of Rubik’s Cube scientific metaphors, reduction algorithms, characteristic applications, and mechanism issues. Finally, the applications and prospects of Rubik’s Cube in the field of mechanism are discussed.
基金the National Natural Science Foundation of China(Grant No.51775473)the Natural Science Foundation of Hebei Province(Grant No.E2018203140).
文摘The mechanism of three⁃order Rubiks 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.
基金the support of the National Natural Science Foun-dation of China(Grant No.12202084)the the Fundamental Re-search Funds for the Central Universities(Grant No.2024CDJXY009)+8 种基金the support of the National Natural Science Foundation of China(Grant No.12372127)the Fundamental Research Funds for the Central Uni-versities(Grant No.2022CDJQY-004)Chongqing Natural Science Foundation(Grant Nos.CSTB2024NSCQ-JQX0028 and CSTB2023NSCQ-LZX0083)the support of the National Natural Science Foundation of China(Grant No.12202085)the China Postdoctoral Science Foundation Funded Project(Grant No.2022M720562)the Special Fund for Postdoctoral Research Project of Chongqing(Grant No.2021XM3022)the support of the National Natural Science Foundation of China(Grant No.12302190)the Science Foundation of the National Key Laboratory of Science and Technology on Advanced Composites in Spe-cial Environments(Grant No.JCKYS2023603C018)the support of the EIPHI Graduate School(Grant No.ANR-17-EURE-0002).
文摘As part of the 4th industrial revolution,programmable mechanical metamaterials exhibit great application potential in flexible robotics,vibration control,and impact protection.However,maintaining a programmed state without sustaining the external stimulus is often challenging and leads to additional energy consumption.Inspired by Rubik’s cube,we design and study an in-situ programmable and distribution-reconfigurable mechanical metamaterial(IPDR-MM).A matrix model is developed to model IPDR-MMs and describe their morphological transitions.Based on this model,the reinforcement learning method is employed to find the pathways for morphological transitions.We find that IPDR-MMs have controllable stiffness across several orders of magnitude and a wide range of adjustable anisotropies through morphology transformation.Additionally,because of the independence of the directions of morphology transformation and bearing,IPDR-MMs exhibit good stability in bearing and can readily achieve high stiffness.The Rubik’s cube-inspired design concept is also instructive for other deformable structures and metamaterials,and the current version of the proposal should be sufficiently illustrative to attract and broaden interdisciplinary interests.
文摘在明确耕地细碎化(cultivated land fragmentation,CLF)会造成的消极和积极影响基础上,构建CLF评价体系,探索以因地制宜为理念差异化解决CLF现象的方法。以陕西省2020年耕地利用现状为例,从耕地的自然资源禀赋、空间聚集程度、利用便利程度三个方面构建陕西省CLF程度三维魔方模型,对其CLF空间分异特征进行探索,并提出了改善CLF的策略。结果表明:陕西省CLF指数(CLFI)总体上呈现中间低、南北高的空间特征,CLFI最大值为0.796,最小值为0.020,均值为0.217,高值集中在陕南和关中交界的秦巴山区以及陕北东部地区。基于CLF特征和农业种植多样性、地区经济水平等影响因素以及耕地资源3个属性特征,提出了针对陕西省CLF的优化分区规划,其中包括保持提升区、集约归并区、设施优化区、资源改造区、综合提升区、综合整治区6类乡镇级引导分区,及以地区社会经济指标为基础划分的政策倾向区、加强整治区、资源倾向区、资源适配区4类县级引导分区,并结合两类分区结果的特征提出了不同地区土地整治的主要方向及关键问题。
