Non-Minimum Phase Zeros in the Dynamics of Flexure Mechanisms

柔性机构采用弹性变形而不是滚动或滑动关节来提供沿某些柔性方向的引导运动。它们在一些实际应用中是必不可少的，包括精密运动平台和扫描仪，因为它们的无关节结构简单，缺乏摩擦和间隙，零组装和维护。在所有这些应用中，都希望实现大运动范围和高速度，以提高吞吐量和生产率。但是，由于缺乏对多轴柔性机构动力学的充分理解，同时实现大范围和高速度仍然是一个挑战。该研究项目将产生克服这种权衡所需的科学知识，从而在各种实际应用中取得突破。特别是，这些科学知识将被用于实现基于柔性的精密运动平台，具有前所未有的性能，用于下一代晶圆检测工具。这些工具，用于半导体制造行业，可以潜在地帮助提高一个数量级的检测过程吞吐量。此外，该项目将有助于向大学生和工业工程师传播动力学、控制和机电一体化方面的理论知识和实践技能。此外，将为当地的科技博物馆创建一个新的互动展览，以激发和激励K-12儿童。多轴柔性机构在实现大位移和动态性能的同时，面临着诸多挑战。大位移导致几何非线性随位移而变化。目前还不清楚哪些非线性是临界的，哪些可以忽略。多轴挠性机构通常采用对称或周期拓扑结构来增强准静态性能，从而产生多个紧密间隔的模态。此外，不可避免的制造公差导致了参数的不确定性。随着位移变化的几何非线性、拓扑对称性引起的紧密间隔模态以及制造公差引起的参数不确定性共同导致在某些条件下挠性机构的频率响应中出现复杂的非最小相位零。这些复杂的非最小相位零点导致了大位移和动态性能之间的严重权衡。这些复杂的非最小相位零何时以及为何出现？这些零可以被分析预测吗？它们有物理意义吗？是否有办法通过物理/控制系统设计来抑制或克服它们的有害影响？所有这些问题目前都没有答案，并且代表了柔性动力学知识的空白，将通过本研究项目来解决。

Flexure mechanisms employ elastic deformation instead of rolling or sliding joints to provide guided motion along certain compliant directions. They are indispensable in several practical applications including precision motion stages and scanners because of their joint-less simple construction, lack of friction and backlash, and zero assembly and maintenance. In all these applications, there is a desire to achieve large motion range as well as high speed to improve throughput and productivity. But achieving large range and high speed, simultaneously, remains a challenge due to a lack of adequate understanding in dynamics of multi-axis flexure mechanisms. This research project will generate the scientific knowledge needed to overcome this tradeoff, leading to breakthroughs in various practical applications. In particular, this scientific knowledge will be leveraged in realizing flexure-based precision motion stages, with unprecedented performance, for the next-generation wafer inspection tools. These tools, used in the semiconductor manufacturing industry, can potentially help improve inspection process throughput by an order of magnitude. Additionally, this project will help disseminate theoretical knowledge and practical skills in dynamics, controls, and mechatronics, among university students as well as industry engineers. Furthermore, a new interactive exhibit will be created for a local science and technology museum to excite and inspire K-12 children.There are several challenges in simultaneously achieving large displacement and dynamic performance in multi-axis flexure mechanisms. Large displacements result in geometric nonlinearities that vary with the displacement. It is not clear which nonlinearities are critical and which ones may be ignored. Multi-axis flexure mechanisms also commonly employ symmetric or periodic topologies to enhance quasi-static performance, which results in multiple closely spaced modes. Furthermore, unavoidable manufacturing tolerances lead to parametric uncertainty. Together, geometric nonlinearities that vary with displacement, closely spaced modes due to topological symmetry, and parametric uncertainty due to manufacturing tolerances give rise to complex non-minimum phase zeros in the frequency response of flexure mechanisms under certain conditions. These complex non-minimum phase zeros result in severe tradeoffs between large displacement and dynamic performance. When and why do these complex non-minimum phase zeros appear? Can these zeros be analytically predicted? Do they have a physical meaning? Is there a way to suppress them or overcome their detrimental effects via physical/control system design? All these questions are currently unanswered and represent a gap in the knowledge on flexure dynamics that will be addressed via this research project.