# Kinematic Analysis and Verification of a New 5-DOF Parallel Mechanism
## 1 Introduction  
Parallel mechanism (PM) can be defined as a closed-loop mechanism in which the moving platform and the fixed platform are connected by at least two independent kinematic chains. The mechanism has two or more degrees of freedom and is driven in parallel. Common parallel mechanisms are Delta and Stewart. Unlike traditional series structure, parallel structure is widely used in automobile, mechanical manufacturing [1; 2; 3; 4; 5], aviation [6], medical treatment [7], electronic manufacturing [8], education, and other fields due to its small cumulative error, high precision, light weight of moving part, high speed, fast dynamic response, compact structure, high rigidity, and large bearing capacity [9; 10; 11; 12]. At present, scholars at home and abroad have done much research on parallel mechanism with few degrees of freedom [13; 14; 15]. [PERSON] [16] proposed a new U-PRU-PUS parallel mechanism solar tracking device with two degrees of freedom, analyzed its singular position, and optimized its motion range. Compared with the solar tracking device with series mechanism, it improved its anti-interference ability, load capacity, and stability to the environment. [PERSON] [17] put forward a new 3-DOF multi-turn center 3-PUU parallel mechanism, analyzed its motion characteristics using screw theory, obtained the Jacobian matrix of 3-PUU parallel mechanism by establishing inverse kinematic equation, determined the singular type of mechanism by analyzing Jacobian matrix, and obtained its workspace by using inverse kinematic method. [PERSON] et al. [18] proposed a 3-UPR parallel mechanism and solved its inverse kinematics problem and forward kinematics problem. The Jacobian matrix is calculated to estimate the singular position of the mechanism. The parameters of the mechanism are optimized. In conclusion, scholars have done more research on 3-DOF parallel robots and less on 5-DOF parallel robots. 5-DOF parallel robot is an important class of low-degree-of-freedom parallel mechanism. It is more flexible than 3-DOF parallel robots and has asimpler structure and easier control than 6-DOF parallel robots. It has good application prospects in cutting, grinding, and 3D printing of parts with complex spatial surfaces. [PERSON] et al. [19] have studied the forward kinematics and inverse kinematics of 4-SPR-SPR parallel mechanism with five degrees of freedom and the causes of vibration when the mechanism works. [PERSON] et al. [20] proposed a new 4-UPS-RPS space parallel mechanism, which can achieve three degrees of freedom of rotation and two degrees of freedom of translation. The rigid body dynamic model of parallel mechanism is established and analyzed. [PERSON] et al. [21] put forward a new type of five DOF parallel robot structure, deduced the inverse kinematics model and forward kinematics model of the mechanism, and applied it to medical equipment. With the development of parallel mechanism, the analysis of singularity and optimization of workspace of parallel mechanism has become a hot research topic. [PERSON] [22] used a \(4\times 4\) Jacobian matrix to analyze the singularity of a spatial 4-DOF parallel mechanism; [PERSON] et al. [23] analyzed the singular configuration of a 4-DOF parallel robot by using the screw theory; [PERSON] et al. [24] analyzed the singularity of a 4-RRCR parallel mechanism using screw theory; [PERSON], [PERSON] [25] used a numerical based algorithm to determine the singular points within the workspace of the 3-PRUS mechanism by determining points where the determinant of the Jacobian becomes zero; [PERSON] [26] analyzed the singularity of two kinds of 3-DOF parallel robots by using the Grassmann line geometry method; [PERSON] et al. [27] analyzed singularities of a partially decoupled generalized parallel mechanism for 3T1R motion; [PERSON] et al. [28] developed system design methodology (LIDeM) for reducing interference among links and increasing workspace of mechanism; [PERSON] et al. [29] optimized 3-PUU parallel mechanism modules for different application objectives.