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

Abstract

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 μ m × 112 μ m × 123 μ m and the resonance frequency of 682 Hz × 687 Hz × 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.