摘要
随着天文学的发展,望远镜的分辨率要求越来越高,对副镜的支撑提出了更高的要求,传统的四翼梁式支撑结构可以实现自动调焦,但不能主动校正副镜的姿态,因此,设计具有两个转动一个移动自由度的副镜支撑机构,实时、稳定、高精度地调整副镜相对主镜的焦距和姿态,具有重要的现实意义。
本文以望远镜副镜三自由度并联支撑为背景,围绕三自由度并联机构的设计主线,开展了构型设计与选型、运动学设计、精度分析与设计、结构参数优化设计、仿真平台设计等五方面的研究。
并联机构的设计首先需要进行构型设计和选型。根据期望两个转动和一个移动自由度的需求,采用约束螺旋理论设计了三支链、采用添加约束法设计了四支链对称的三自由度并联机构。在此基础上,综合考虑并联机构的结构对称、结构简单、结构紧凑、低惯性等定性指标,以及伴随运动小、全局条件数大、运动副刚度大精度好等定量指标,最终选取3-RCU构型作为望远镜副镜并联支撑。
本文提出分类建模方法,建立两转一移三自由度并联机构的统一运动学模型、速度传递模型和误差传递模型。根据并两转一移三自由度并联机构的驱动和约束特性,分类建立了运动学模型；在此基础上,建立了运动支链的D-H矩阵模型,全面反映各运动支链的运动副和杆件的运动特性；建立了并联机构的速度传递模型,反映驱动速度与动平台的有效位姿变化速度之间的映射关系,并得到机构的速度Jacobian巨阵和全局条件数。同时,对并联机构的姿态描述进行了深入讨论,引入zxz欧拉角法研究机构的伴随运动和姿态空间,引入YXY欧拉角法研究机构速度Jacobian矩阵、全局条件数和误差传递模型。
考虑并联机构具有两个转动一个移动自由度,定义了两个欧拉角和一个移动的微小摄动为机构的有效位姿误差,基于误差摄动原理和机构的速度传递模型,建立了运动副安装误差(包括结构偏差)、运动副间隙误差和支链驱动误差(包括传感误差)等主要误差源到动平台有效位姿误差的全误差模型；然后,推导了3-RCU并联机构的最大误差模型,分析了各主要误差源对动平台有效位姿误差的误差灵敏度；最后,分别研究了基于灵敏度和基于成本的3-RCU并联机构精度设计,并采用遗传算法实现了3-RCU并联机构的精度设计。
根据两转一移三自由度并联机构的运动特点,推广了机器人包含工作空间和全姿态工作空间的概念,定义了两转一移并联机构的可达工作空间和灵活工作空间,以及工作空间体积；然后讨论了并联机构的约束条件,并基于区间分析方法计算了3-RCU并联机构的工作空间,分析了工作空间的形状特点。
确定以动平台半径、连杆中心位置长度和驱动行程与静平台半径的比值为设计变量,分析了全局条件数、最大位姿误差和工作空间体积等3个性能指标随3个设计变量的变化规律,优化设计得到3-RCU并联机构的关键结构参数。
最后,利用Matlab GUI工具箱设计了两转一移三自由度并联机构仿真平台,重点研究了3-RCU并联机构的可视化运动仿真模块。基于SolidWorks软件建立了机构的三维实体模型,基于SimMechanics工具箱设计了机构的运动学和动力学控制系统,包括轨迹规划模块、控制器模块、并联机构模型模块和显示模块等,实现了3-RCU并联机构的可视化运动仿真研究。
With the advancement of Astronomy, and the continuously increasing requirements of telescopes resolution, the study of support for the secondary mirror is highly desirable. The traditional support structure, which is a four-wing beam framework, can realize automatic focal distance adjustment, while active adjustment of secondary mirror posture is not possible. It has strong practical application to have a supporting system for the telescope secondary mirror to modulate focal distance and posture in a real-time, stable, and high accuracy manner. Three degrees-of-freedom (DoFs) parallel mechanisms have high accuracy, large loading capacity, and these potentials can be explored in the area of telescope supporting system.
This dissertation concentrates on design of some three DoFs parallel mechanism for the telescope secondary mirror support. The type synthesis and selection, kinematics model and analysis, accuracy analysis and synthesis, structure parameter optimization, and design of simulation platform are presented. The results provide analytical and statistical support for the telescope system.
Firstly, type synthesis and selection is presented. Symmetric three-chain and four-chain parallel mechanisms with two rotational DoFs and one translational DoF (2R1T) are designed based on constrained screw theory. The3-RCU structure is chosen as the support structure for the telescope secondary mirror considering its symmetry, simplicity, compact structure, low inertia, high overall conditional number, high stiffness and high accuracy of kinematics pairs.
Secondly, unified kinematics models of these2R1T parallel mechanisms are built based on classification modeling method. Driving models are built considering that the input can change the length of chain or the position of the kinematics pairs that connect the moving platform and the base. Constrained models are built for cases where the constrained force line vector of each chain can be parallel to the moving platform or to base. Then, the D-H matrix model is built to express chain and kinematics pair moving attributes. Velocity transfer model is also derived to show the mapping between driving speed and moving platform posture speed, the Jacobian matrix, and global conditional number.
The attitude description of the2R1T parallel mechanisms is deeply analyzed. The zxz Euler angel approach is taken to describe the attitude to solve the prismatic motion and attitude workspace. Then YXY Euler angel approach is considered to describe the attitude to study the velocity Jacobian matrix, the global condition number and the error transfer model.
Thirdly, the efficient error model is proposed as the perturbation of the two Euler angels and one translation, under consideration of that all these parallel mechanisms have two rotational and one translational DoFs. The error perturbation theory and velocity transformation model are used to derive the mapping from joint installation errors (including the structural deviations), the joint clearances and the driving errors (including sensing errors) to the pose error of moving platform. Based on this model, the largest pose error and the sensitivity for each main error source can be calculated for the3-RCU parallel mechanism. Moreover, the accuracy synthesis is performed for3-RCU parallel mechanism based on sensitivity and manufacturing cost, respectively. And the Genetic Algorithm is introduced to realize the accuracy synthesis.
Fourthly, the definition of the robot workspace is generalized for the2R1T parallel mechanisms. The accessible workspace, flexible workspace, and the workspace volume of the2R1T parallel mechanisms are defined, and the constraints are discussed. The workspace characteristics of the3-RCU parallel mechanism are presented and discussed using interval analysis method.
Fifthly, the ratios of the key structural parameters and the radius of the base are chosen to be the design variables. The key structural parameters include the radius of the moving platform, the chain length at equilibrium position, and the driving stroke. These parameters are optimized by analyzing the overall conditional number, largest pose error and the volume of the workspace.
Finally, the simulation platform for the2R1T parallel mechanisms is built on Matlab GUI toolbox, and the kinematics and dynamic simulation are conducted and shown. The3-D model is built using SolidWorks, and the control system is designed using SimMechanics, including trajectory planning block, controller block, parallel mechanism model block, and display block.
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