Constraint and Mobility Change Analysis of Rubik’s Cube-inspired Reconfigurable Joints and Corresponding Parallel Mechanisms

(2020) 33:81 Li et al. Chin. J. Mech. Eng. https://doi.org/10.1186/s10033-020-00500-z Chinese Journal of Mechanical Engineering Open Access ORIGINAL ARTICLE Constraint and Mobility Change Analysis of Rubik’s Cube-inspired Reconfigurable Joints and Corresponding Parallel Mechanisms Duanling Li1,2, Pu Jia1,3* , Jiazhou Li1,3, Dan Zhang4 and Xianwen Kong5 Abstract The current research of reconfigurable parallel mechanism mainly focuses on the construction of reconfigurable joints. Compared with the method of changing the mobility by physical locking joints, the geometric constraint has good controllability, and the constructed parallel mechanism has more configurations and wider application range. This paper presents a reconfigurable axis (rA) joint inspired and evolved from Rubik’s Cubes, which have a unique feature of geometric and physical constraint of axes of joint. The effectiveness of the rA joint in the construction of the limb is analyzed, resulting in a change in mobility and topology of the parallel mechanism. The rA joint makes the angle among the three axes inside the groove changed arbitrarily. This change in mobility is completed by the case illustrated by a 3(rA)P(rA) reconfigurable parallel mechanism having variable mobility from 1 to 6 and having various special configurations including pure translations, pure rotations. The underlying principle of the metamorphosis of this rA joint is shown by investigating the dependence of the corresponding screw system comprising of line vectors, leading to evolution of the rA joint from two types of spherical joints to three types of variable Hooke joints and one revolute joint. The reconfigurable parallel mechanism alters its topology by rotating or locking the axis of rA joint to turn all limbs into different phases. The prototype of reconfigurable parallel mechanism is manufactured and all configurations are enumerated to verify the validity of the theoretical method by physical experiments. Keywords: Reciprocal screws, Reconfigurable-axis (rA) joint, Metamorphic parallel mechanism, Constraint analysis 1 Introduction In recent years, the reconfigurable mechanism [1] has become a development trend of mechanisms adapted to different requirements and environments. This has led to other developments in the kinematic mechanism and metamorphic mechanisms with the ability to change mobility. Metamorphic mechanism [2] is derived from the concept of metamorphosis in the sense of evolutionary design. Its metamorphic principle mainly depends on the change of geometric or physical constraints, which can change its own topological structure and subsequent *Correspondence: 1 School of Automation, Beijing University of Posts and Telecommunications, Beijing 100876, China Full list of author information is available at the end of the article mobility. Zhang et al. [3] analyzed the rule extension of embedded spatial model with metamorphic characteristics to develop metamorphic operations. Four types of branching singularities are identified by Gogu [4] from the new formula of mobility, connectivity, overconstraint and redundancy of parallel robots. Kong et al. [5‒7] presented a method for the type synthesis of parallel mechanisms with multiple operation modes. Gan et al. [8‒12] proposed three kinds of metamorphic parallel mechanisms composed of three limbs with reconfigurable Hooke joints, and the unified kinematics analysis of a new 3rTPS metamorphic parallel mechanism were investigated. Zhang et al. [13‒15] proposed a kind of metamorphic parallel mechanism extracted from origami fold and analyzed the evolutionary kinematic configuration changes of two metamorphic parallel mechanisms © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativeco mmons.org/licenses/by/4.0/. Li et al. Chin. J. Mech. Eng. (2020) 33:81 of 3SvPSv. A new type of reconfigurable modular parallel robot was proposed by Carbonari et al. [16], which is equipped with a locking system to fix one of the revolute joints and is able to perform different types of motion, especially pure translation and pure rotation. Ye et al. [17‒19] proposed a family of reconfigurable parallel mechanism with reconfigurable hybrid limbs based on diamond kinematic chain. The reconfigurable parallel mechanism has ability to perform variable motion modes, such as 3T, 2T1R, 2R1T and 3R. Wang et al. [20] proposed a new reconfigurable parallel mechanism based on a reconfigurable spatial five bar mechanism with two different working modes, which can realize four kinds of motions. Qu et al. [21] analyzed the topology and mobility of a novel redundant reconfigurable parallel mechanism. Wang et al. [22] investigated the application of parallel leg mechanism in Quadruped/bipedal reconfigurable walking robot. Tian et al. [23, 24] investigated the structural synthesis of a class of reconfigurable parallel mechanisms based on closed-loop metamorphic linkage and five bar metamorphic linkages. Song et al. [25] proposed a new type of 6R metamorphic mechanism with eight motion branches and multiple bifurcation points, and explained the transformation of kinematic branches by kinematic curves. The metamorphic rT joint mentioned in Ref. [8] consists of two revolute joints which are perpendicular to each other. Besides, one of the revolute joint axes can not only rotate independently as a revolute joint, but also be used to adjust the spatial position of another. However, the mobility of the joint is constant. It changes the mobility of the limb only by linear dependent with other revolute joints. Although the vA joint mentioned in Ref. [13] has ability to realize the mobility change from spherical joint, Hooke joint and revolute joint, there is only one type of equivalent motion joint, especially in the configuration of equivalent spherical joint. Since the phase of equivalent spherical joint can not form three-axis vertical spherical joint, the working space of metamorphic parallel mechanism composed of vA joint will be limited. The rA joints proposed in this paper can not only alter the mobility of joint, but also the mobility of the constructed limbs and mechanisms. In addition, it formed a variety of different types of spherica (...truncated)