# Kinematics and Performance Analysis of the 2T1R/1T2R Reconfigurable Decoupled Parallel Mechanism
## 1 Introduction  
Reconfigurable parallel mechanisms can adapt to different task requirements by changing their structural configurations. [1, 2]. Compared to traditional parallel mechanisms, reconfigurable parallel mechanisms have significant advantages in terms of their variable structural characteristics and good adaptability [3]. They can precisely compensate for the shortcomings of traditional parallel mechanisms with a fixed degree of freedom (DOF) and a single operating mode in practical operations, and can meet the practical needs of multiple tasks and complex working conditions [4, 5, 6]. In recent years, with the development of robot technology and the related needs of complex multi-operating conditions, reconfigurable parallel mechanisms have become one of the hot spots for domestic and foreign robot researchers [7, 8, 9]. [PERSON] et al. [10] proposed a reconfigurable mobile robot based on a four-bar parallel mechanism, which can adapt to different road conditions by changing its geometric shape and topology to have three motion modes. [PERSON] et al. [11] designed a variable topology-reconfigurable mobile parallel robot based on the idea of branching changes in mobile parallel mechanisms. The robot can achieve seven gait motion modes through topologyreconstruction, and conduct corresponding experimental analysis on each gait to verify the theoretical rationality. [PERSON] et al. [12] built a novel multi-mode mobile robot based on Schatz linkages, which consists of four Schatz linkages. By basing the design of the motion compensation link on Schatz linkages, the robot can realize three motion modes. The steering and payload experiments of the robot are carried out to verify the rationality of the design. [PERSON] et al. [13] presented a two-degree-of-freedom eight-legged mobile robot with a reconfigurable torso. The walking platform is constructed using an integral closed-chain mechanism, which consists of multiple sets of planar closed-chain leg mechanisms and spatial single closed-chain torso mechanisms, and realizes steering, climbing, and rolling behaviors by using mechanism reconstruction. The feasibility and performance of the mechanism's movement are verified by experiments. [PERSON] and [PERSON] [14] developed a novel reconfigurable prismatic mobile robot with eight motion modes, which has various characteristics of a mobile robot and can switch between multiple motion modes such as bipedal, rolling, creep, and track movement through deformation, and can move in various complex terrains. [PERSON] et al. [15] were inspired by origami folds and proposed a metamorphic kinematic pair. They introduced the metamorphic kinematic pair into a kinematic chain and topologically changed the kinematic chain, resulting in a series of multi-loop metamorphic mechanisms with phase transition and direction switching functions. The foldability of such mechanisms was experimentally verified. [PERSON] et al. [16] analyzed a novel reconfigurable parallel mechanism consisting of three SvPS-series kinematic branches, where the spherical variable-axis (Sv) kinematic pair is a reconfigurable kinematic pair that switches between the U pair and R pair by changing the axis direction. The parallel mechanism can be used as the structure of a reconfigurable robot machining center to adapt to changing task requirements. [PERSON] et al. [17] drew inspiration from fortune tellers' origami and equivalently transformed individual origami units into spherical 4R mechanisms, and finally designed a motion steering 8R metamorphic mechanism to build a novel reconfigurable mobile robot. [PERSON] and [PERSON] [18] designed a novel discontinuous movable 6R mechanism based on the theory of Lie group and Lie algebra. By changing the orientation of the R-axis to achieve different connection modes, two different kinematic modes were formed.