2-UPR-PRU并联机构静刚度模型建立与性能分析

针对2-UPR-PRU两转一移三自由度并联机构，采用螺旋理论和应变能方法对其进行系统的静刚度模型建立与性能分析。基于闭环矢量法建立2-UPR-PRU并联机构的运动学逆解模型。考虑分支杆件的柔性，采用螺旋理论和应变能方法推导2-UPR-PRU并联机构各分支的刚度矩阵，结合变形协调方程构建2-UPR-PRU并联机构的整体刚度矩阵，得到外载作用下机构在不同位型的变形情况和整体柔度矩阵，并通过ANSYS软件进行数值仿真验证。基于静刚度模型分析2-UPR-PRU并联机构的虚功刚度指标，获得2-UPR-PRU并联机构在不同外载和操作高度情况下的静刚度性能分布图谱。研究结果对于设计样机、提高机构的控制精度方面有重要的参考价值。

Elastostatic Stiffness Modeling and Performance Analysis of 2-UPR-PRU Parallel Manipulator

Parallel manipulators with two rotations and one translation have been attracted the interest from both academic and industry. They can be selected as parallel modules and used in the workpieces machining. A systemic stiffness modeling and performance analysis of a 2-UPR-PRU three degrees of freedom parallel manipulator was presented based on the screw theory and strain energy, where U, P and R denoted universal, prismatic and revolute joint, respectively. Firstly, the inverse kinematics of the 2-UPR-PRU parallel manipulator was presented by using the closed-loop method. Next, considering the compliances of limbs, the stiffness matrices of limbs in the 2-UPR-PRU parallel manipulator were derived through the screw theory and strain energy, and the overall stiffness matrix of the parallel manipulator was obtained by combining the deformation compatibility equations. Under the external wrench, the deformations and overall compliance matrix of the 2-UPR-PRU parallel manipulator in different configurations were obtained, and a numerical simulation based on the ANSYS software was used to verify the correctness of the theoretical result. Finally, the distributions of virtual-work stiffness index were used to evaluate and discuss the stiffness performances of the 2-UPR-PRU parallel manipulator in different external wrenches and operational heights. The stiffness modeling and performance analysis of the 2-UPR-PRU parallel manipulator can provide an important reference for the design of prototype and the high precise control of system.