新型副镜并联调整机构非线性特性及校正  

Nonlinear characteristic and correction for new-style parallel adjustment mechanism of secondary mirror

作　　者：叶宇[1,2,3] 乐中宇 顾伯忠[1,2] 杨世海 Ye Yu;Yue Zhongyu;Gu Bozhong;Yang Shihai(National Astronomical Observatories/Nanjing Institute of Astronomical Optics&Technology,Chinese Academy of Sciences,Nanjing 210042,China;CAS Key Laboratory of Astronomical Optics&Technology,Nanjing Institute of Astronomical Optics&Technology,Nanjing 210042,China;University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院国家天文台南京天文光学技术研究所,江苏南京210042 [2]中国科学院天文光学技术重点实验室(南京天文光学技术研究所),江苏南京210042 [3]中国科学院大学,北京100049

出　　处：《红外与激光工程》2020年第1期222-230,共9页Infrared and Laser Engineering

基　　金：国家自然科学基金(11503060);中国科学院天文财政专项(2911C09700)。

摘　　要：为满足望远镜副镜结构定位精度的要求,提出一种固定杆长杆端轴向平移运动模式的六杆并联机构。从微分几何的观点研究了该机构输入关节空间向量与输出工作空间向量之间的非线性运动学特性,并采用曲率概念度量解轨迹的非线性弯曲。通过与雅可比矩阵的对比分析可知,采用曲率度量并联机构的非线性和采用雅克比矩阵反映的瞬时线性性质一致,所设计的副镜并联调整机构在整个运动行程范围内的最大非线性误差约为3.15μm。测试结果表明:采用多项式误差曲线拟合校正之后,该副镜调整机构三维平移重复定位精度小于2.6μm,二维旋转重复定位精度小于1.8″,满足实际望远镜观测的需要,采用的曲率度量法也可以为其他并联机构的非线性分析和校正提供一种新的思路。In order to meet the structure positioning accuracy requirements of the telescope secondary mirror, a fixed length rod end axial translational motion model of hexapod was proposed. From the point of view of differential geometry, the nonlinear kinematics between the input joint space vector and the output workspace vector of the mechanism was studied, and the curvature concept was used to measure the nonlinear bending of the trajectory. Comparing with the Jacobian matrix, it was found that the curvature of the parallel mechanism was consistent with the instantaneous linear property reflected by the Jacobian matrix. The maximum nonlinearity error of the designed secondary mirror parallel adjustment mechanism was about 3.15 μm in the whole motion range. The test results show that after the polynomial error curve fitting correction, the three-dimensional translational repeating positioning accuracy of the secondary mirror adjustment mechanism is less than 2.6 μm, and the two-dimensional rotation repeat positioning accuracy is less than 1.8″, which meet the needs of actual telescope observation. At the same time, the curvature metric method can also provide a new idea for the nonlinear analysis and correction of other parallel mechanisms.

关 键 词：并联调整机构 非线性特性 曲率 误差校正 雅可比矩阵 

分 类 号：TH751[机械工程—仪器科学与技术]