An analytical investigation on the new design of 3-DOF flexible nanopositioner driven by electrostatic actuators
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TECHNICAL PAPER
An analytical investigation on the new design of 3-DOF flexible nanopositioner driven by electrostatic actuators A. Naderi Rahnama1 • M. Moghimi Zand1,2 • M. Mousavi Mashhadi1 Received: 14 February 2020 / Accepted: 9 April 2020 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract 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 9 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.
1 Introduction Flexure-based nanopositioning systems are important and useful tools in hi-tech applications such as micro-microscopes, nanotechnology, lithography, nano and micro equipment, and the nanostructured assembly equipment. This equipment usually has high-precision positioning and high-speed displacement in order of kHz, improving their performance is still at the forefront of many types of research. According to Fig. 1, in which a flexible positioning mechanism moving in two directions XY is shown (Awtar and Slocum 2007), it is observed that in the nanopositioning system, the elastic motion of the stage is created & M. Moghimi Zand [email protected] 1
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
2
Small Medical Devices, Bio-MEMS and LoC Lab, School of Mechanical Engineering, University of Tehran, Tehran, Iran
using flexible beams. To create a greater r
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