针对望远镜副镜姿态和焦距自动调整的需求, 设计了副镜三自由度并联支撑机构构型, 分析了它们的运动学特性并讨论了构型的选取。首先, 基于约束螺旋理论, 设计了对称三支链两转一移并联机构的构型; 根据副镜支撑运动副尽可能少、低惯性、直线驱动等要求, 选取了12种可行构型。然后, 针对12种可行构型, 根据驱动输入特点和支链约束特性, 提出分类建模思想, 并建立了统一运动学模型; 引入ZXZ欧拉角法描述机构姿态, 简化了姿态空间和伴随运动的表达和分析方式。最后, 以1.2 m口径望远镜系统为例, 仿真研究了副镜并联支撑机构的伴随运动。结果表明, 支链约束力线矢平行静平台的7种构型具有更小的伴随运动, 不大于0.27 mm。该项研究为后续的精度和刚度特性研究提供了基础。

To realize tip/tilt and focus adjustment for a telescope secondary mirror, several types of parallel support systems were designed and their dynamic characteristics and construct selection were analyzed. First, the screw theory was used to realize the type synthesis for 2R1T (two-rotation and one-translation degrees of freedom) parallel mechanisms with 3 symmetrical branches. 12 types of feasible mechanisms with the fewest joint in each branch, the smallest inertia and linear actuators were selected for the support systems. Then, the selected mechanisms were classified according to the actuating characteristics and constraint properties and the kinematics models were established respectively, including actuation models and constraint models. Moreover, ZXZ Euler angels were introduced to describe the orientation of moving platform and to simplify the description and analysis of orientation and parasitic motion for 2R1T parallel mechanisms. Finally, a 1.2 m telescope was taken as an illustrative example to calculate the parasitic motion induced by the constraints. The results indicate that 7 types of mechanisms with constraint force parallel to the static platform have smaller parasitic motions no more than 0.27 mm. The kinematic model and design results provide theory basis for the following analysis on accuracy and stiffness.