Modular kinematics and statics modeling for precision positioning stage

Compliant amplifying mechanisms and guiding mechanisms are prevalently adopted in most present piezo-actuated precision positioning stages. By considering the coupled relations among piezoelectric actuator, compliant amplifying mechanism and guiding mechanism, an analytical method towards the statics modeling of the kinematic performance for precision positioning stages is presented. In this method, these three parts are separately modeled and coupled together in series by defining input/output stiffness. Then two static displacement models with different stiffness definitions are established and mathematically proved to be equivalent, both of which may be versatile for practical applications. A comparison of the proposed method with the finite element analysis for a flexure-based XY positioning stage reveals less than 10% deviations and indicates that the workspace significantly decreases with consideration of the finite stiffness of piezoelectric actuator and the elastic effect of guiding mechanism. The proposed method offers a modular and assembled statics modeling tool for analysis and design of a wide class of flexure-based precision positioning stages.