三维桥式放大机构的柔性微定位平台的研究与改进

Research and Improvement of Flexible Micro-positioning Platform with a Three-dimensional Bridge-type Amplification Mechanism

在微定位平台的设计中,引入能够产生高位移放大倍数的三维桥式放大机构,并在此基础上引入了能够有效减少输出端寄生位移的四杆对称式导向机构,从而使所设计的微定位平台能够充分结合二者优势。根据应变能理论、卡氏第二定理、拉格朗日定理,建立该微定位平台的静动态数学模型,理论分析了平台关键尺寸对平台位移放大倍数的影响;并通过计算获得了最优参数下的放大倍数和固有频率,其值分别为19.90和193.26 Hz。通过有限元方法验证了放大倍数和固有频率,其相对误差分别为4.3%和5.9%,从而证明了所改进的微定位平台的优越性能以及理论分析方法的准确性,为放大机构的柔性微定位平台的数学模型构建提供了一定的理论指导。

In the design of the micro-positioning platform,a three-dimensional bridge-type amplification mechanism capable of generating high displacement amplification ratio was introduced.On this basis,a four-bar symmetric guiding mechanism was incorporated to effectively reduce the parasitic displacement at the output end.This design allows the micro-positioning platform to fully leverage the advantages of both mechanisms.By applying the strain energy theory,the second theorem of Castigliano,and Lagrange's theorem,the static and dynamic mathematical models of the micro-positioning platform were established.The theoretical analysis revealed the influence of key dimensions on the displacement amplification ratio of the platform.Through calculation,the amplification ratio and natural frequency were determined to be 19.90 and 193.26 Hz respectively,under the optimal parameters.Finite element analysis was used to verify the amplification ratio and natural frequency,resulting in relative errors of 4.3%and 5.9%respectively.This confirms the superior performance of the improved micro-positioning platform proposed in this study,as well as the accuracy of the theoretical analysis method.It provides theoretical guidance for the mathematical modeling of flexible micro-positioning platforms with amplification mechanisms.