Enhanced mathematical modeling of the displacement amplification ratio for piezoelectric compliant mechanisms

Piezo-actuated, flexure hinge-based compliant mechanisms have been frequently used in precision engineering in the last few decades. There have been a considerable number of publications on modeling the displacement amplification behavior of rhombus-type and bridge-type compliant mechanisms. However, due to an unclear geometric approximation and mechanical assumption between these two flexures, it is very difficult to obtain an exact description of the kinematic performance using previous analytical models, especially when the designed angle of the compliant mechanisms is small. Therefore, enhanced theoretical models of the displacement amplification ratio for rhombus-type and bridge-type compliant mechanisms are proposed to improve the prediction accuracy based on the distinct force analysis between these two flexures. The energy conservation law and the elastic beam theory are employed for modeling with consideration of the translational and rotational stiffness. Theoretical and finite elemental results show that the prediction errors of the displacement amplification ratio will be enlarged if the bridge-type flexure is simplified as a rhombic structure to perform mechanical modeling. More importantly, the proposed models exhibit better performance than the previous models, which is further verified by experiments.