冗余驱动2SPR-2RPU并联机构的运动静力学 及奇异性研究

针对打磨、抛光等重载机器人的应用需求，提出了一种新型冗余驱动2SPR-2RPU并联机构。运用螺旋理论计算了2SPR-2RPU并联机构的自由度，并求解了其运动学逆解与速度雅克比矩阵。全面考虑2SPR-2RPU并联机构自身重力因素，利用拆杆法对该机构进行静力学分析，并建立了其静力学模型。针对机构驱动冗余的特点，运用拉格朗日乘数法，以驱动力最小为目标构造函数，对驱动力进行分配求解，获得2SPR-2RPU并联机构在给定运动轨迹下的驱动力变化趋势。根据速度雅克比矩阵对2SPR-2RPU并联机构的奇异性进行分析，结果表明该机构没有运动学正解奇异和运动学反解奇异，但具有2个运动学混合奇异，且2个混合奇异位形可通过合理设计机构杆件尺寸进行规避。研究结果可为实际工程应用中冗余驱动并联机构的研究提供一定的理论基础。

Research on kinematic statics and singularity of redundant drive 2SPR-2RPU parallel mechanism

Aiming at the application requirements of heavy-duty robots for grinding and polishing, a new redundant drive 2SPR-2RPU parallel mechanism was proposed. The degree of freedom of the 2SPR-2RPU parallel mechanism was calculated by using the screw theory, and the inverse kinematics and Jacobian matrix of the parallel mechanism were solved. Considering the gravity factor of 2SPR-2RPU parallel mechanism, the statics analysis of the mechanism was carried out by the method of dismantling the bar, and its statics model was established. Aiming at the characteristics of drive redundancy, the Lagrangian multiplier method was used to construct the target function with the minimum driving force, and the driving force was distributed and solved. The driving force variation trend of the 2SPR-2RPU parallel mechanism with the given motion track was obtained. According to the velocity Jacobian matrix, the singularity of 2SPR-2RPU parallel mechanism was analyzed. It was concluded that the mechanism had no forward kinematics singularity and inverse kinematics singularity, but only two mixed kinematics singularities, and the two singularities could be avoided by reasonable design of the rod size. The research results can provide a theoretical basis for the study of redundant drive parallel mechanism in practical engineering applications.