Design And Experiment Of A Precision Positioning Stage For Nanoimprint Lithography

In order to develop a precision positioning stage for nanoimprint lithography, this dissertation deals with the key issues relevant to mechanical design, kinematic modeling, stiffness analysis, static and dynamic modeling and kinematic calibration. As a result, a prototype machine of 3-DOF piezo-driven compliant stage has been developed. The following research achievements have been completed. Replacing the revolute joints of the modified DELTA mechanism with single-axis flexure hinges and adjusting the length of the links, a new-type precision positioning stage with three translation degrees of freedom has been achieved. Three piezoelectric actuators are used to carry out the passive position adjustment of the platform.The Pseudo-Rigid-Body (PRB) Model methodology is utilized to investigate the kinematical characteristics of the stage, and two kinds of PRB models with effsets and non-effsets are developed. By the homogeneous coordinate transformation methodology and the vector-loop equation respectively, the forward and inverse kinematics modeling are achieved. The comparison of the two PRB model is done by the finite element simulation and the PRB model with non-effsets is adopted for the subsequent works. The workspace of the stage is evaluated in term of the constraints due to the allowable rotation range at the flexure hinges. And in order to achieve a maximum workspace subjected to the given dexterity indices, kinematic optimization of the design parameters is carried out, which results in a stage satisfying the operational requirements.Considering the energy stored as elastic deformation of the flexure hinges and the gravitational potential of the platform and the links, the stiffness at driving point of the active arm is modeled based on the Castigliano's first theorem. For the influence of the stiffness of the compliant prismatic pair, that constructed as a planar four-bar parallelogram, in the flexure-based precision positioning stage, the mathematics model of the stiffness matrix of the compliant prismatic pair is established using the compliant matrix and matrix transformation method. Discussions are developed about the influences of the constraints and the compliance of the connecting rods on the flexibility characteristics of the prismatic pair, the geometric parameters are changed to show the variation of stiffness. After that, the system stiffness of the flexure-based stage is analytically modeled on the same methodology, and the influence of the geometry parameters on three stiffness factors has been graphically evaluated as well. Furthermore, the finite-element simulation has been undertaken to validate the analytical model.The static analysis of the compliant stage has been studied on the principle of virtue work, the influence of the mass of the platform and the links and the stiffness of the flexure hinges on the position of the platform are discussed. The dynamic modeling has been performed on the principle of virtue work and the Lagrangian equation respectively. The influences of the mass of the platform and the links and the stiffness of the flexure hinges on the driving torques are analyzed, and the numerical simulations with different movement modes are presented to verify the validity of both models. The natural frequencies are analyzed with the variation of the geometry parameters and the stiffness of the flexure hinges.The imperfect error characteristics of the stage such as the modeling and calculating errors, geometric errors of flexure hinges and links caused by machining imperfections, assembling errors, gravity's effect are analyzed and discussed on the kinematic model deduced by the recursive matrix methodology, The all-parameter-error-identification model of the compliant stage is setup, and the computer simulation is made.Experiments results about the kinematics, the static compliance characteristics and the natural frequency confirmed that the mathematic modeling and the relative theoretic analysis is creditable.