Design and trajectory tracking of a nanometric ultra-fast tool servo

This paper reports on the development of a piezo-actuated nanometric ultra-fast tool servo (NU-FTS) for nanocutting. For motion guidance, a flexure mechanism is especially designed using a novel kind of generalized flexure hinges with the notch profiles described by a rational Bezier curve. Both kinematics and dynamics properties of the mechanism are comprehensively modeled through a novel finite beam modeling method. With this model, the hinge is divided into a set of serially connected beams with constant cross sections. The equivalent stiffness and lumped moving mass of the mechanism are derived based on the Euler-Bernoulli beam theory. Taking advantage of the structure and performance model, the notch shape as well as the dimensions are optimized to achieve the specified criteria for the NU-FTS. Performance of the designed mechanism is verified through both finite-element analysis and practical testing on a prototype. Overall, the NU-FTS is demonstrated to have a stroke of 6 and 1.2 μm for the quasi-static and 10 kHz driving condition, respectively. Through dynamics inversion-based trajectory preshaping, a maximum following error around 25 and 50 nm is obtained for tracking a simple harmonic and a complicated trajectory, respectively.