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

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.