An analytical investigation on the new design of 3-DOF flexible nanopositioner driven by electrostatic actuators

With the increasing development of nanopositioning stages, the study of their deformation and instability under various actuators is very important. Accordingly, in the present paper, the nanopositioning mechanism based on flexible links with the ability to move in three directions of XYZ is introduced using an electrostatic actuator. Then, using the analytical method, static behavior and performance of this mechanism under the influence of electrostatic force are studied. For this purpose, part of this mechanism, which includes a flexible beam with the electrostatic force, is considered. Then, using the nonlinear Euler–Bernoulli beam theory and taking into account the nonlinear effects arising from the radius of curvature, for the first time, the nonlinear differential equation is extracted. Applying the step-by-step linearization method and assuming the static voltage applied to the end of the flexible beam, the effect of different parameters on static deformation is investigated. The results of this study show that considering the nonlinear effects caused by curvature radius has a significant effect on the mechanical behavior of the system, and with increasing the value of this parameter, the hardening behavior of the flexing beam increases. This reduces the static deflection of the flexible beam in comparison with the results of linear theory. Also, by increasing the voltage applied to the flexible beam, the created nonlinear strains are increased, and the nonlinear effects of the radius of curvature become significant. For example, with an increase in the dimensionless bending stiffness parameter from 0 to 10 × 10−3, the maximum deflection of the flexible beam for 10 V, 15 V, and 20 V voltages decreases by 7.7%, 35.8%, and 48.6%, respectively.