In this paper, the kinematics, dynamics, and load distribution algorithm of a 4-PPPS redundantly actuated parallel manipulator are investigated with the screw theory. For the forward kinematic analysis, we propose the major joint set, a minimum set for determining the kinematic and dynamic state of the mobile platform with six specially selected prismatic joints. The reciprocity of screws is applied for simplifying the derivation of the Jacobian matrix. The driving forces of the active joints are solved with the principle of virtual work for the non-redundant and the fully redundant actuation mode with the major joint set. For the fully redundant actuation mode, to avoid joint overload resulted from the conventional least-norm load distribution solution, to smooth the force transition, and to increase the positioning accuracy of the manipulator, a load distribution algorithm based on Lagrange optimization is proposed. These effects are achieved by means including reducing the deformations of the z-axis links and considering the sensitivity and elasticity of major joints. At last, the effectiveness of the modeling method and the proposed algorithm is verified with a case study.

在本文中，利用螺旋理论研究了 4-PPPS 冗余驱动并联机械手的运动学、动力学和负载分配算法。对于正向运动学分析，我们提出了主要关节集，这是一个最小集，用于确定具有六个特别选择的棱柱关节的移动平台的运动学和动力学状态。螺钉的互易性用于简化雅可比矩阵的推导。主动关节的驱动力采用非冗余的虚功原理和主关节组的全冗余驱动方式求解。对于全冗余驱动方式，避免了传统的最小范数载荷分配方案导致的关节过载，平滑力的过渡，提高机械手的定位精度，提出了一种基于拉格朗日优化的负荷分配算法。这些效果是通过包括减少 z 轴链接的变形和考虑主要关节的敏感性和弹性等手段来实现的。最后，通过案例研究验证了建模方法和所提算法的有效性。