# Optimal Design for a Novel Compliant XY Platform Integrated with a Hybrid Double Symmetric Amplifier Comprising One-Lever and Scott–Russell Mechanisms Arranged in a Perpendicular Series Layout for Vibration-Assisted CNC Milling

## TL;DR

This paper presents a new compliant XY platform design for vibration-assisted CNC milling, optimized for precise positioning and surface quality.

## Contribution

A novel hybrid displacement amplifier combining lever and Scott–Russell mechanisms in a perpendicular series layout for vibration-assisted CNC milling.

## Key findings

- The hybrid design achieved a primary natural frequency of 308.79 Hz with a 3.04% difference between theoretical and FEM results.
- The Firefly optimization algorithm improved the mechanism's design parameters effectively.
- Vibration-assisted milling at 400 Hz produced a surface roughness of 0.187 µm.

## Abstract

Compliant mechanisms are often utilized in precise positioning systems but have not been thoroughly examined in vibration-aided fine CNC machining. This study aims to develop a new 02-DOF flexure stage for vibration-aided fine CNC milling. A hybrid displacement amplifier, featuring a two-lever mechanism, two Scott–Russell mechanisms, and a parallel leading mechanism, was integrated into a symmetric perpendicular series configuration to create an innovative design. The pseudo-rigid body model (PRBM), Lagrangian approach, finite element analysis (FEA), and Firefly optimization algorithm were employed to develop, verify, and optimize the quality response of the new positioner. The PRBM and Lagrangian methods were used to construct an analytical model, while finite element analysis was used to validate the theoretical solution. The primary natural frequency results from theoretical and FEM methods were 318.16 Hz and 308.79 Hz, respectively. The difference between these techniques was 3.04%, demonstrating a reliable modelling strategy. The Firefly optimization approach applied mathematical equations to enhance the key design factors of the mechanism. The prototype was then built, revealing an error of 7.23% between the experimental and simulated frequencies of 331.116 Hz and 308.79 Hz, respectively. The specimen was subsequently mounted on the fabricated optimization positioner, and vibration-assisted fine CNC milling was performed at 100–1000 Hz. At 400 Hz, the specimen achieved ideal surface roughness with a Ra value of 0.187 µm. The developed design is a potential structure that generates non-resonant frequency power for vibration-aided fine CNC milling.