2UPR-RPU过约束并联机构刚度性能评价

运用螺旋理论和应变能方法研究了具有2R1T三自由度的2UPR-RPU过约束并联机构的静弹性刚度性能,模型考虑了杆件和关节的柔度。首先,基于螺旋理论得到分支的约束螺旋系;其次,基于材料力学得到分支中杆件的应变能,通过映射分支约束螺旋系到铰空间得到关节的应变能,通过汇总杆件、关节的应变能和卡氏定理得到与约束螺旋系对应的分支紧凑刚度矩阵;最后,通过虚功原理得到机构的总体刚度矩阵。采用有限元商业软件建立了有限元模型,并与理论模型进行对比,验证了理论模型的正确性。定义弹性元件存储的应变能与总应变能之比作为应变能因子指标,给出了应变能因子指标在规则工作空间的四维切片分布图,从应变能的角度定量评价了各弹性元件对机构刚度性能的影响程度,给出了不同载荷作用下的全局应变能因子指标。本研究为定位对机构刚度性能影响最大的弹性元件提供了新的思路。

Stiffness Performance Evaluation of 2UPR-RPU Over-constrained Parallel Mechanism

The elastostatic stiffness modeling of a 2UPR-RPU parallel manipulator with 2R1T three degrees of freedom was studied based on the screw theory and strain energy, considering the compliance of the bars and joints. Firstly, the limb constraint wrenches was formulated based on the screw theory. Secondly, the strain energy of bar was formulated by material mechanics, and joint by mapping the constraint wrenches to the joint space, and concentrated limb stiffness matrix corresponding to the constraint wrenches was thus obtained by summarizing the strain energy of bars and joints in the limb, and combining with the Castigliano second theorem. Finally, the overall stiffness matrix was assembled based on the virtual work principle. The theoretical result was verified by commercial ANSYS software. The strain energy factor index was defined as the strain energy of the elastic component account for total strain energy for illustrating the influence of each elastic component on the stiffness performance of the mechanism. A four dimensional image of slice distribution was presented, the influence of each elastic element on the stiffness performance of the 2UPR-RPU parallel mechanism was quantitatively evaluated from the perspective of strain energy. Finally, the global strain energy factor indices of the mechanism under different external wrenches were presented to find the elastic component with the maximum compliance. The proposed modeling provided a new ideas for improving the stiffness performance of the mechanism more effectively.