Generalized element-node complete model and its implementation for the optimal design of a piezo-actuated compliant amplifier

Compliant amplification mechanisms are widely applied to extend the stroke of stacked piezoelectric actuators. Accurate modeling of static and dynamic performances is crucial for the optimal design of complex compliant mechanisms. By generalizing the planar element-node model-based finite element method, this paper proposes a new modeling method capable of describing the spatial complete kinetostatics and dynamics for compliant mechanisms. On the basis of the widely reported complete compliance models for flexure hinges, a versatile stiffness model is established for the hinge with an arbitrary notch shape through the force equilibrium model. The generalized model is then demonstrated by applying for modeling and optimizing a compliant mechanism with dual-stage amplification. The verification through finite element simulations suggests that the maximum modeling error for the kinetostatic and first six resonant frequencies for the mechanisms with and without structural optimizations is less than 20%. Finally, the open-loop and closed-loop performance tests on the prototype with optimized parameters are conducted, demonstrating the effectiveness of the developed modeling and optimization methods.