Design and control of flexure based XYϑZ stage

This article presents the design and control of an ultraprecision XYϑZ stage with nanometer accuracy. The stage has a plane mechanism and symmetric hexagonal structure which consists of a monolithic flexure hinge mechanism with three piezoelectric actuators and six flexures preserving the plane motion. The symmetric design reduces the effect of temperature gradient on the structure. Because the relationship between design variables and system parameters are quite complicated and there are some trade-offs among them, it is very difficult to set design variables manually and optimal design procedure is used. The objective of design is maximizing the 1st resonant frequency to improve the dynamic characteristics. The reason is that the stage must move with heavy load of about 20 kg. The higher resonant frequency also makes the stage stiffer and stronger against the dynamic force and moment. This paper describes the procedures of selecting parameters for the optimal design and a mathematical formulation for the optimization problem. The stage was designed to attain ±10 um in the X- and Y-direction and ±90arcsec in the yaw direction at the same time and have the 1st resonant frequencies of 455.5 Hz in X- and Y-direction and 275.3 Hz for yaw direction without load. The stage was fabricated according to the optimal design results and experimental results indicate that the design procedure is effective. A conventional PI control results are presented for ultraprecision motion.