2UPR-RRU并联机构及其运动学分析

针对航天制造中轻金属材料搅拌摩擦焊的焊接需求，提出一种以2UPR-RRU构型的1T2R三自由度并联机构为主要执行机构的焊接装备。基于螺旋理论分析了该构型在一般位型和特殊位型下的约束螺旋系和自由度性质，指出该构型是具有两转一移的全周自由度机构。建立2UPR-RRU并联机构运动学模型，利用闭环矢量法建立动平台位姿与各驱动支链的关系，推导其运动学的正反解；在正解过程中构造优化目标函数，采用粒子群优化（PSO）算法分析了位姿输出与驱动关节输入的关系，得到了驱动输入的精确解。基于输入/输出速度雅可比矩阵分析了机构的奇异性问题，指出该构型避免存在驱动奇异的条件，研究表明该机构具有较好的运动学特性和驱动特性，具备良好的应用潜力。 

2UPR-RRU parallel mechanism and its kinematic analysis

To actualize the requirement of friction stir welding for light metal materials in aerospace manufacturing, this paper proposed a novel 2UPR-RRU parallel mechanism with IT2R 3-DOF as the manipulator of the welding equipment. Based on screw theory, the mechanism of one translational and two rotational full-cycle DOFs was found on general position and special position. Kinematic model of 2UPR-RRU parallel mechanism was constructed. Then the relationship between platform's positions and driving joints was analyzed by closed loop vector method and forward/inverse kinematics solutions were deduced. The optimal objective function was established in the process of forward kinematics, particle swarm optimization (PSO) algorithm was used to analyze the relationship between platform outputs and driving joints inputs, and finally the exact solution was found. Based on the input/output velocity Jacobi matrix, the motion singularity of 2UPR-RRU was analyzed, and especially the conditions to avoid driving singularity were discussed in detail. The research shows that 2UPR-RRU parallel mechanism, which is an important full-cycle DOF mechanism, possesses excellent kinetic characteristics, driving characteristics and high potential application.