Mathematical modelling and experimental study of a novel planar micro-positioning stage using shape memory alloy actuators

The application of smart materials as actuators in precise positioning systems has witnessed significant growth in recent years. However, the use of shape memory alloy (SMA) materials in this context is hindered by their slow response and complex nonlinear behaviour. To overcome these limitations, this paper introduces a novel approach that incorporates two opposite SMA actuators into a flexure hinge type micro-positioning stage, aiming to enhance the system speed. A semi-analytical modelling approach is employed to model the nonlinear behaviour of the SMA actuator. Using the available material models for SMA materials and the nonlinear curved beam theory, the governing equations of the proposed SMA actuator are derived and the resulted partial differential equations are reduced to an algebraic equation based on the Galerkin method. The resulting equations are then solved using the return map method. To validate the accuracy and effectiveness of the proposed model, an experimental setup is constructed. The experimental results demonstrate the model ability to accurately predict the behaviour of the system. Additionally, the developed model allows for the extraction of stress and strain profiles of the SMA actuators for designing the actuator. The study highlights the potential of integrating the proposed model with robust control methods for future works, aiming to effectively control micro-positioning systems and further enhance their performance.