4UPS/UPR并联机构刚度特性分析

针对耦合型4UPS/UPR少自由度并联机构，分析了其自由度及耦合运动特性，给出了其旋量形式的一、二阶影响系数。借助于虚功原理及旋量形式的一、二阶影响系数，推导了4UPS/UPR并联机构包括外力、重力及非广义关节驱动力的静力学方程。通过对静力学方程微分，建立了机构完整的柔度模型，并以此为基础推导了其方向刚度模型，给出了方向刚度极值存在的必要条件。分析了机构位姿、铰链点尺度参数及坐标系选择对方向刚度特性的影响，并给出了相应的数值算例进行验证。

Stiffness Characteristics of a 4UPS/UPR Parallel mechanism

For the coupling 4UPS/UPR limited degree-of-freedom parallel mechanism, its degree-of-freedom and the coupling motion characteristics are analyzed, and the first and second order influence coefficient of screw form are given. Referring to the principle of virtual work and the first and second order influence coefficient of screw form, the statics equation of 4UPS/UPR mechanism including external force, gravity and non-generalized joint drive is derived. Through the differential of the statics equation, a complete flexibility model is given. On this basis, the direction stiffness model was deduced, and the necessary existence condition of the extreme direction stiffness is given. The influence of pose, hinges parameter and coordinate selection on the direction stiffness characteristics of the mechanism is analyzed, and the corresponding numerical examples is given to demonstrate the above theory.