基于3-RRR结构的光学元件柔顺微动调整机构的位姿正解

针对光刻投影物镜中光学元件X/Y/θ微动调整的工程需求,研制了一种基于3-RRR结构的光学元件柔顺微动调整机构,并对其位姿正解进行了研究。建立了3-RRR柔顺并联机构的伪刚体模型,并采用矢量代数法理论推导了该机构的位姿正解,得到了它的理论雅克比矩阵。然后,在NASTRAN中建立了3-RRR柔顺并联机构的有限元模型,得到了仿真环境下该机构的位姿正解和雅克比矩阵。最后,对研制的3-RRR柔顺并联机构进行了实验研究,得到了该机构真实的位姿正解和雅克比矩阵。实验结果表明,实验雅克比矩阵的各项系数分别为0.577 7、-0.304 0、-0.283 3、0.002 1、0.524 6、-0.516 5、1.402 6、1.481 9、1.435 3,而理论雅克比矩阵相对应的各项系数分别为0.612 9、-0.3065、-0.306 5、0、0.530 8、-0.530 8、1.444 6、1.444 6、1.444 6,得到的数据表明:采用矢量代数法能够理论推导出该机构正确的位姿正解公式。提出的3-RRR柔顺微动调整机构位姿正解方法为微动调整机构的研制提供了设计依据。

Forward kinematics of 3-RRR flexure parallel mechanism used in lens micro-adjustment

To meet the requirements of X/Y/θ adjustment in a lithography projection lens, a 3-RRR flexure parallel mechanism used in lens micro-adjustment was developed and its forward kinematics was researched. Firstly, the pseudo-rigid body model of the 3-RRR flexure parallel mechanism was established, the forward kinematic solution of the 3-RRR parallel mechanism was derived based on vector mathematical theory, and its theoretical Jacobian matrix was obtained. Then, the Finite Element Model(FEM) of the 3-RRR parallel mechanism was established in NX NASTRAN environment, and the FEM forward kinematic solution and the FEM Jacobian matrix were obtained. Finally, according to the experiment of the 3-RRR flexure parallel mechanism, the actual forward kinematic solution and the actual Jacobian matrix were acquired. The experiment results show that: the parameters of the actual Jacbian matrix are 0.5777, -0.304 0, -0.283 3, 0.002 1, 0.524 6, -0.516 5, 1.402 6, 1.481 9, 1.435 3,while the parameters of the theoretical Jacbian matrix are 0.612 9, -0.306 5, -0.306 5, 0, 0.530 8, -0.530 8, 1.444 6, 1.444 6, 1.444 6, respectively. The experiment results demonstrate that the forward kinematics can be exactly derived by the vector mathematical theory. The forward kinematic equation method for the 3-RRR flexure parallel mechanism is feasible when designing micro-motion mechanisms.