Theoretical modeling of attenuated displacement amplification for multistage compliant mechanism and its application

With the merits of multiplying displacement amplification ratio and compact structure, flexure-based multistage compliant mechanisms have been widely proposed in recent ten years. Experimental output displacement, however, is attenuated more or less in various designs and is even reduced to less than 10% of the original ambitious design in some prototypes. In this paper, the issue on attenuated displacement amplification of multistage compliant mechanisms is theoretically investigated. A formula of displacement amplification ratio is established based on the elastic beam theory and by defining an impedance factor, which describes the hindering effect of the second layer on the preceding layer. The high accuracy of the model is verified by finite element analysis with no more than 5% deviations. It allows a designer to quickly get an intuitional sense of why the output displacement is attenuated and how each parameter affects the mechanisms' performance. Thanks to the theoretical guidance, a new planar two-stage compliant mechanism with relatively high frequency response and large range as well as no assembly error is designed and tested. Experiments show a natural frequency of 3.3 kHz in the output direction and displacement of 198 μm, which agrees with the theoretical prediction.