Analytical model of a single stage compliant mechanism with flexible lever beam

Abstract

Compliant micromechanisms are employed in the design of MEMS to amplify force or displacement. Models of compliant mechanism generally assume that its lever beam is rigid and does not experience deformation. In most cases, this assumption is acceptable since the lever beams are designed wide enough so that they undergo minimal deformity when transferring force or displacement from input to output; however, in some cases, the lever beam not only is the mechanical interface between its input and output, but it also couples them electrically and/or thermally. Therefore, it may be desirable to design the lever beam as thin as possible to reduce the coupling between the input and output systems. Consequently, the assumption of a rigid beam is no longer valid for calculating the amplification factor. In this paper, the assumption of the rigidity of the lever beam is relaxed to develop an analytical model for a compliant mechanism having a flexible lever beam. The results obtained using the flexible beam model, in contrast with the rigid beam model, shows very good agreement with the finite element model. For wide levers, the results of the flexible beam and the finite element models approach to those of rigid beam model. These results show that the amplification factor of a flexible lever beam is less than a rigid one. The reason is that the flexible lever beam absorbs a fraction of input energy in the form of elastic strain energy. Without significant loss of accuracy, this model can replace the finite element model to improve the computation time in the optimization procedure to achieve higher amplification factor and lower electrical/thermal coupling.