Reconfigurable configuration model and bifurcation motion characteristics of Rubik’s Cube mechanism

Abstract

There are several Rubik Cube types; their internal structure is complex, making them harder to understand, analyze, and design. Since the Rubik’s Cube is a complex mechanism consisting of a large number of parts, its reconfigurable theory and bifurcation characteristics need to be studied. Thus, this paper first presents the piece matrix for each Rubik’s Cube piece based on its motion characteristics, taking the classic third-order Rubik’s Cube and Square-1 Rubik’s Cube as examples. This allows the authors to explain the meaning of elements within the piece matrix. The Rubik’s Cube reconfigurable configuration model is established next, and its reconfigurable motion model and the associated configuration are given. The Rubik’s Cube reconfigurable motion model in any configuration is obtained by using the transformation matrix. The Rubik’s Cube bifurcation characteristics are analyzed on the basis of reconfigurable configuration model. The work at hand improves the existing reconfigurable theory of Rubik’s Cube mechanism and offers beneficial classification cubes to the subsequent research and synthesis.