3PRS/UPS冗余驱动并联机器人刚度特性分布

设计提出了一种采用冗余驱动的3PRS/UPS三自由度并联机器人，并建立分析其机构模型.基于螺旋理论，对并联机器人进行运动学分析，通过分别针对机构的驱动和约束建立了雅可比矩阵，最后整合建立了包含冗余驱动在内的全雅可比矩阵.利用虚功原理，结合并联机器人驱动副和约束副的柔度影响，推导得出了机构全刚度矩阵.同时，分析了机构在给定静载荷条件下的变形情况，总结出机构的空间变形分布规律.使用刚度矩阵的最小、最大特征值和运动刚度指标（KSI，Kinematic Stiffness Index）为机构刚度评价指标，对比和分析了引入冗余驱动前后对并联机器人刚度特性分布的影响，得出冗余驱动支链的引入可提高并联机器人特定方向的刚度和改善刚度分布的结论，为冗余驱动并联机器人优化设计和开发应用奠定基础. 

Stiffness characteristics distribution of 3 PRS/UPS parallel manipulator with actuation redundancy

A three degree of freedom (DOF) 3PRS/UPS parallel manipulator with actuation redundancy was designed and investigated. The architectural model was constructed and the kinematic analysis was presented based on screw theory. The overall Jacobian matrix including redundant actuation was derived through respectively establishing the actuation and constraint Jacobian matrices. The overall stiffness matrix was derived by virtual work principle, in which the compliances subject to actuators and constraints were involved. The deformation of manipulator under static load was calculated, and its distribution rule was established. Utilizing the extremun eigenvalue of stiffness matrix and kinematic stiffness index (KSI), the stiffness performance of the manipulator was evaluated. The influence to the stiffness characteristics distribution of the manipulator after introducing redundant actuation was compared and analyzed. It was concluded that the redundant actuation can increase the stiffness along specific axis and improve its stiffness characteristics distribution, which will be valuable for the architecture design of a parallel manipulator with actuation redundancy.