Performance Analysis And Optimal Design Of A Class Of Parallel Mechanisms With3Degrees Of Freedom

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.