Planar mechanism is a kind of important mechanism, which plays a key role in daily life and industrial life. This paper presents a new synthesis method for planar Rubik’s cube mechanism (PRCM). Firstly, the composition and motion mechanism of the PRCM are introduced combined with a symmetrical four-axis PRCM. The reconfigurable motion process of two kinds of PRCMs is described and analyzed, and the conditions of realizing reconfigurable motion of PRCMs are obtained. Next, a new synthesis method of PRCM is put forward, and the detailed process and flow chart of PRCM synthesis are given. Then, the factors affecting the topological structure of the PRCM are determined from the synthesis process. Finally, the cases of each type of PRCM are synthesized by setting specific parameters. The PRCM synthesis method is of great significance to perfect and enrich the plane reconfigurable mechanism synthesis theory.

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.

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In order to improve the obstacle-crossing ability, motion stability and load-bearing capacity of mobile robots for different terrains, the Rubik's Cube mechanism (RCM) with strong coupling and variable topology is introduced into the field of mobile robots, and a wheel-legged mobile robot (WLMR) based on RCM is proposed. Aiming at the problems of the classical three-order RCM, such as small internal space, difficult processing and demanding precision, a new type of chute third-order RCM is designed, and its mechanical characteristics analysis and feasibility analysis are carried out. What's more, a driving configuration analysis method is established according to different driving configuration relationships, and the configuration of WLMR is determined by the configuration stability analysis. Then, a WLMR with polymorphism is designed, and gait planning and gait stability analysis are conducted. Eventually, the cosimulation and prototype experiments are performed to verify the efficiency of the WLMR's straight motion, in-situ rotation, obstacle-crossing and morphology transformation in complex environments. This research not only provides a reference for the design of polymorphous mobile robots, but also opens up ideas for the application of the RCM in daily production and life.

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