# Design and Analysis of a Two-Degree-of-Freedom Inertial Piezoelectric Platform

## TL;DR

This paper introduces a new piezoelectric platform for precise leaf stomatal detection, combining large motion range and high resolution.

## Contribution

A novel 2-DOF cross-scale piezoelectric platform with a 3-DOF stator is proposed to improve detection of leaf stomata.

## Key findings

- The platform achieves a motion range of 15 mm × 15 mm with high resolution.
- Displacement resolutions reach 11.39 nm and 13.61 nm in X and Y directions.
- The platform successfully detects leaf stomatal density, showing potential for botanical micro-detection.

## Abstract

Leaf stomatal density directly regulates the rates of gas exchange and water loss and is a core indicator of plants’ water-retention capacity and drought adaptability. Because detecting leaves over a macroscopic range requires large-stroke motion, whereas accurate identification of stomata demands high-precision positioning, the operational platform for stomatal-density detection faces the dual challenge of large strokes and high resolution. This paper proposes a novel two-degree-of-freedom (2-DOF) cross-scale piezoelectric platform that employs a new three-degree-of-freedom (3-DOF) piezoelectric stator to address the backlash issue in inertial drive and combines it with finite-element simulation for verification. The prototype of the 2-DOF cross-scale piezoelectric positioning platform is developed, and a series of experiments are conducted to evaluate its performance. The experimental results show a motion range of 15 mm × 15 mm; the displacement backlash rates in the X and Y directions range from 0% to 9.84% and 0% to 28.42%, respectively; and the displacement resolutions reach 11.39 nm and 13.61 nm, respectively. In addition, an application experiment on leaf stomatal-density detection is carried out on the developed 2-DOF platform, demonstrating its potential for botanical micro-detection.