| The innovation of mechanism is the key to the innovative mechanical equipment,and theoretical research is the support.The exploration of the unknown principle of existing mechanism is the indispensable source of inspiration for the innovative design of machinery.Rubik's Cube is widely known as a toy,but its mechanism principle is rarely involved.The Rubik's Cube mechanism is a complex multi-loop coupled mechanism with remarkable characteristics of the metamorphic mechanism.In this paper,the classical third-order Rubik's Cube is taken as the research object,and its mechanical characteristics,topology changes and metamorphic process are studied,which lays the foundation for the establishment of a perfect theoretical system of Rubik's Cube mechanism.The main contents of this paper are as follows:(1)The concepts of three kinds of combined kinematic pairs and equivalent rigid body which can describe the kinematic characteristics of Rubik's Cube mechanism are proposed.The singular characteristics of Rubik's Cube mechanism are also analysed.From the biological point of view,the metamorphic characteristics of Rubik's Cube mechanism are analysed.In this paper,the relationship between sub-pieces of Rubik's Cube mechanism in the movement process is described by mathematical language.At the same time,the relationship between the center piece and other sub-pieces is analysed.(2)Based on the positive combination state and intermediate state,the metamorphic characteristics of the Rubik's Cube mechanism is made a deep discussion on.A more suitable topological description method for Rubik's Cube mechanism is established.Three kinds of topological transformations are summarized.The topological change of the process of the transformation between different configurations of the Rubik's Cube mechanism is described.(3)The description of adjacency matrix which is suitable for the topological representation of Rubik's Cube mechanism is proposed.And the adjacency matrix of the positive combination state of Rubik's Cube mechanism is obtained,and the corresponding element characteristics are also summarized.The adjacency matrix corresponding to different kinds of topological transformation is established,and its element characteristics are summarized.The transformation between the positive combination states of Rubik's Cube mechanism is described by adjacency matrix.Furthermore,the adjacency matrixs of Rubik's Cube mechanism and the intermediate state are optimized.(4)The concept and description method of the transformation matrix of the structure state of Rubik's Cube mechanism are put forward.At the same time,based on basic operation and basic transformation of Rubik's Cube mechanism,all topological descriptions of Rubik's Cube mechanism are analysed and obtained.The unified description equation of the metamorphic process of Rubik's Cube mechanism is established,and the general expression of the basic metamorphic equation of Rubik's Cube mechanism is given.(5)All kinds of sub-pieces of Rubik's Cube mechanism are named in a unified way.From the two aspects of configuration design and scale design,the construction design principle of Rubik's Cube mechanism is studied.The design requirements and configuration design methods of central components are proposed.The scale design is divided into motion dimension design and modeling design,and their characteristics and design requirements are summarized.The above research results on the Rubik's Cube mechanism will be beneficial to the establishment of the theory of Rubik's Cube mechanism,and promote the invention of Rubik's Cube mechanism products and their application in the industrial field. |
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