Design, modeling and control of an XYZ flexure parallel mechanism with large motion range and decoupled kinematic structure

Abstract

With the advantages of no backlash, no accumulative error and compatibility with acuum and clean environment, flexure parallel mechanisms (FPMs) have been employed in high-precision positioning systems in optics, micro/nano scale metrology and manufacturing, semiconductor production and biology applications. This thesis focuses on the study of XYZ-FPMs with decoupled kinematic structure, large motion range and high positioning precision. A new type of prismatic joint is designed, with the advantages of having a large motion range, no parasitic motion, no stiffening, no buckling and a symmetric structure. An exact modeling method of the large-motion prismatic joints is proposed for the stiffness and dynamic models. Structure synthesis of XYZ-FPMs with large motion range and decoupled kinematic structure is studied. Different from the structure synthesis of rigid-body mechanisms, the possible configurations are proposed based on the Screw Theory, with the consideration of limitations and characteristics inherent in flexure mechanisms. In flexure mechanisms, the critical static performances include stiffness, workspace, stage size and parasitic motion. The stiffness models of these synthesized structures are formulated. The definition of motion range is proposed based on the workspace and the stage size. A dimension optimization approach based on these static performances is generalized. Based on these generalized study of flexure mechanisms, a 3-PPP XYZ-FPM with large motion range and decoupled kinematic structure is developed, covering structure design, dimension optimization, exact modeling and robust control. The experimental results show that the 3-PPP XYZ-FPM has a large workspace of 2.3mm × 2.3mm × 2.3mm and a large motion range of 7%. The decoupled kinematic structure is verified, with the maximum cross-axis error of 2% and the maximum parasitic rotation of 1.5mrad. The hybrid position and vibration control algorithm using the H∞-theory solves three common problems of flexure mechanisms, i.e., unmodeled uncertainties due to the difficulty of exact modeling of high-order mode shapes, high sensitivity to the external disturbances, and vibration caused by inherent low damping. Using the designed controller and verified by the experiments, the positioning precision of 0.1μm is achieved, and the settling time is shortened to 0.1s after vibration suppression.