Abstract: Designing Displacement Amplification Mechanism (DAM) is one of the common strategies to enlarge the output displacement of piezoelectric stack actuator and further enlarge the workspace of precision positioning stage and micro-nano-manipulator.For compliant DAMs,how to enlarge the displacement amplification ratio and make the output displacement achieve the expected direction is a keypoint.In this paper,a compliant orthogonal two-stage leverage DAM was designed systematically and analyzed.The demands of kinematic properties for the mechanism and piezoelectric stack actuator were analyzed,and the systematic structural design of compliant orthogonal two-stage leverage DAM was conducted by combining the analysis of freedom degree and rigid body substitution.With the consideration of midpoint drift of the flexure hinges as well as the deformation of beam,the displacement amplification ratio of DAM was modeled statically by using vector polygon,Castigliano's second theorem as well the equations of static equilibrium.Further,based on Monte-Carlo method,the global sensitivity analysis of dimensional parameters in the DAM was conducted.The kinematic synthesis of DAM,the modeling of displacement amplification ratio as well as the sensitivity analysis results were verified by finite element simulation.Based on the results of sensitivity analysis and finite element simulation,the fabrication tolerance of dimensions for the DAM was further designed.The result showed that the proposed displacement amplification ratio modeling and sensitivity analysis method needed not use the condition that the output displacement was orthogonal to the input displacement,which could be applied to the general compliant multi-stage leverage DAM.

Key words: compliant displacement amplification mechanism, kinematic synthesis, midpoint drift, Monte Carlo method, global sensitivity analysis

摘要： 设计位移放大机构是扩大压电叠堆驱动器输出位移,进而提升精密定位平台和微纳操作末端执行器工作空间的常见策略之一。对于柔顺位移放大机构,如何提高位移增益并使输出位移达到预期方向是其研究热点之一。鉴于此,对柔顺正交二级杠杆位移放大机构进行了系统性设计与分析。首先,分析机构与压电叠堆驱动器的运动学特性要求,结合机构自由度分析与刚体替代法,对柔顺正交二级杠杆位移放大机构进行系统性结构设计;然后,考虑柔顺铰链中点漂移与杆件变形,运用矢量多边形、卡氏第二定理与静力平衡方程,对机构位移增益进行静力学建模;进而,基于蒙特卡洛方法,对机构尺寸参数进行全局敏感性分析;最终,利用有限元仿真,对机构运动学综合、位移增益建模以及敏感性分析结果的有效性进行验证,并基于敏感性分析和有限元仿真结果,进一步设计了机构尺寸参数的制造公差等级。所提出的机构位移增益建模与敏感性分析方法无需使用输入输出位移正交的条件,可以推广应用于一般的柔顺多级杠杆位移放大机构。

关键词: 柔顺位移放大机构, 运动学综合, 中点漂移, 蒙特卡洛方法, 全局敏感性分析