Design, Pseudostatic Model, and PVDF-Based Motion Sensing of a Piezo-Actuated XYZ Flexure Manipulator

This paper develops a compact piezo-actuated XYZ flexure mechanism with an integrated polyvinylidene fluoride (PVDF) based displacement sensor. The sensing scheme is, by sticking a shaped PVDF film on the guiding flexible beams and using the kinematic relationship of the clamped-sliding flexible beam, widely available in compliant mechanisms. The optimal shape of PVDF is found by maximizing the sensitivity with an analytical sensing model. A pseudostatic model is also established to predict and optimize the kinetostatics and dynamics of the manipulator without calculating the elastic/kinetic energies or using Lagrange's equation. Thus, the dynamic modeling is simplified as a statics-similar problem. A comparison of the theoretical model with finite-element analysis reveals its high accuracy and substantially concise step. Finally, the manipulator is tested having the stroke range of 112 mu m x 112 mu m x 123 mu m and the resonance frequency of 682 Hz x 687 Hz x 3.88 kHz with relatively large stroke range and high frequency in the Z-motion. Moreover, the experimental output of the proposed PVDF sensor matches well with the laser sensor, providing a new way with ignorable volume, high sensitivity, large bandwidth, and low cost to measure the displacement of compliant mechanisms, in which the space is usually confined and assembling a bulky transducer is difficult.