冗余驱动的三平动并联机构性能分析与优化

提出一种冗余驱动的三平动并联机构。利用李群理论和修正的Grübler-Kutzbach公式对机构的输出自由度进行了分析。建立机构的位置方程，得到位置逆解和正解表达式，分析机构的运动部分解耦特性。推导机构的雅可比矩阵，并进行奇异分析。分析机构的工作空间。采用螺旋理论和虚功原理，建立机构的动力学模型，得到驱动力的优化分配，驱动力理论分析与仿真计算结果最大偏差为0.6%。建立机构的运动学评价指标和动力学评价指标，并研究尺度参数与机构性能间的映射关系。基于性能图谱对机构的尺度参数进行优化，提高其综合性能。

Performance Analysis and Optimization of Redundantly Actuated Three Translational Parallel Mechanism

A novel redundantly actuated parallel mechanism with three translational motion was proposed. It had four kinematic limbs that connected the moving platform to the fixed base. The output degrees of freedom of the mechanism was analyzed by using Lie Group theory and the modified Grübler-Kutzbach criterion. The parallel mechanism had three translational degrees of freedom, four actuated prismatic joints, and thus was redundantly actuated. Position model of the parallel mechanism was established. Inverse position solutions and direct position solutions with analytical expressions were derived. The partially decoupled motion feature of the mechanism was studied. Singularity analysis was conducted based on the derived Jacobian matrix. Workspace of the mechanism was analyzed. Velocity and acceleration of each joint and each part of the parallel mechanism were derived through screw theory. Dynamic model was established by using virtual work approach, through which the optimal joint torques were obtained. A numerical simulation based on the ADAMS software was carried out. The maximum deviation between the theoretical and simulation results was 0.6%, which verified the correctness of the theoretical model. Dexterity index and dynamic manipulability ellipsoid index were used to evaluate the kinematic and dynamic performances of the mechanism. Mapping relationship between the performance and dimensions were investigated. Dimensional optimization was conducted based on the performance atlas, which improved the performance of the mechanism. The proposed parallel mechanism can be used to construct a five axis grinding machine.