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
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.
