On a simplified nonlinear analytical model for the characterisation and design optimisation of a compliant XY micro-motion stage

- A simplified analytical model of a compliant XY micro-motion stage is proposed.
- The model takes into account the nonlinear bending of the compliant beams.
- The model requires significantly less computation time than FEA.
- The model is useful for design optimisation of parallelogram-based compliant stage.
- The results are in accordance with the Finite Element Model (FEA) and experimental results.

Compliant micro-positioning stages offer low-cost high precision and repeatability but limited workspace and nonlinear behaviour. The conventional modelling techniques used to characterise micro-motion stages are often either complex or inaccurate for large displacements. New methods have recently been developed with satisfying results. However, the presented models often focus on one part of the stage characterisation. This paper presents an analytical model used to characterise a compliant XY micro-motion stage in terms of stiffness and working range, taking into account the stress and buckling limitations, motion loss and parasitic displacements. The presented model combines a 6-degree-of-freedom (DOF) linear model and a simplified 2-DOF nonlinear static model. As a case study, this model is used for the design of a micro-motion stage which is intended to be the fine positioning system for a hybrid miniaturised product assembly system. The results generated by the analytical model, the finite element analysis (FEA) and the experimental testing are all in agreement. The analytical model is therefore proven to be suitable for a full characterisation and design optimisation; reducing the computation time from a few hours to a few minutes when using MATLAB rather than FEA software. Its ability to predict the output displacement as a function of the input displacement with a maximum error of less than 2% also makes it suitable for open-loop control. The travel range of the fabricated stage is greater than ±2.3 mm2 and the maximum cross-coupling error is less than 2.5%.