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 $ \mu $m 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.

中文翻译：

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纳米级超快刀具伺服的设计与轨迹跟踪

本文报告了用于纳米切割的压电驱动纳米超快速刀具伺服 (NU-FTS) 的开发。对于运动引导，特别设计了一种挠性机构，使用一种新型广义挠性铰链，其凹口轮廓由有理贝塞尔曲线描述。该机构的运动学和动力学特性都通过一种新颖的有限梁建模方法进行了综合建模。在这个模型中，铰链被分成一组具有恒定横截面的串联梁。该机构的等效刚度和集总运动质量是基于欧拉-伯努利梁理论推导出来的。利用结构和性能模型，优化缺口形状和尺寸以达到 NU-FTS 的指定标准。通过有限元分析和原型的实际测试验证了设计机构的性能。总的来说，NU-FTS 被证明在准静态和 10 kHz 驱动条件下分别具有 6 和 1.2 $\mu $m 的行程。通过基于动力学反演的轨迹预整形，分别获得了25和50 nm左右的最大跟随误差，用于跟踪单谐波和复杂轨迹。