Study On The Law Of Motion Transformation Of Third Order Rubik’s Cube Mechanism

The exploration and research of new mechanism is the source of mechanical equipment upgrading.Rubik’s Cube is well known as a toy,but few scholars have studied it as a metamorphic mechanism with variable topology and strong coupling.However,due to the lack of theoretical guidance,the innovation and application of Rubik’s Cube mechanism are seriously hindered.Taking the third-order classic Rubik’s Cube as the research object,this paper aims to establish a mathematical description system of Rubik’s Cube and its motion,and study the law of Rubik’s Cube motion transformation under this system,so as to provide a theoretical tool for the research of Rubik’s Cube and lay a theoretical foundation for the application and development of this kind of metamorphic mechanism.The main contents of this paper are as followsThis paper studies the mathematical description of the configuration of Rubik’s Cube metamorphic mechanism;by analyzing the composition structure of Rubik’s Cube,the composition elements of the description of Rubik’s Cube configuration are determined,and on this basis,the concept of theme is put forward,so as to determine the description of sub block and its position;the rotational symmetry of sub block is analyzed,and the direction description and operation rules of sub block are established;the topological structure of Rubik’s Cube is studied,and then the related problems are put forward The mapping relationship between the incidence matrix and the Rubik’s Cube configuration is established,and all the operations of the Rubik’s Cube are summarized based on the operation of the rotation layer.In this paper,the forward and inverse kinematics of Rubik’s Cube metamorphic mechanism are deeply studied;the mapping relationship between Rubik’s Cube operation and displacement is analyzed,and the improved rotation expression is obtained by adding direction lines on the basis of rotation expression;the mapping relationship between Rubik’s Cube operation and group is established,and the order and non transitive group of group are introduced to deeply study the motion transformation of each rotation;the essence of Rubik’s Cube configuration transformation is analyzed.Then,the mathematical model of the positive solution of the Rubik’s Cube is established;the judgment rules of the existence of the structure state are established by using the characteristics of parity and sub block direction transformation,and the mathematical model of the inverse solution of the Rubik’s Cube is established by using the idea of equivalence.This paper studies how to create the reduction method.Firstly,it summarizes the common theoretical methods of constructing the reduction formula,and analyzes the hidden equivalent properties and identity properties in the Rubik’s Cube operation sequence.Secondly,based on several classic reduction methods,it extracts the commonness of the Rubik’s Cube reduction method,and establishes the reduction model of the reduction idea and the reduction formula.Finally,it analyzes the characteristics of the operation operator,and puts forward some suggestions According to the idea of returning the direction of the atomic block first and then the position of the atomic block,the reduction formula of each step is solved by using the trajectory planning method.To explore the application of Rubik’s Cube mechanism,and build the first prototype;based on the cycle characteristics and metamorphic characteristics of Rubik’s Cube mechanism,summarize the three application scenarios of Rubik’s Cube mechanism,establish the relationship between theoretical research and application level,and point out the difficulties of Rubik’s Cube mechanism application;design the mechanical structure and control system of Rubik’s Cube prototype based on its own structure and the needs of industrial production field,According to the operation of the prototype,the improvement direction of the next generation prototype is determined.The above research results of Rubik’s Cube mechanism motion transformation will provide a theoretical basis for Rubik’s Cube research,deepen the understanding of the scientific laws hidden in Rubik’s Cube itself,and promote the application of Rubik’s Cube mechanism in the field of mechanical production.