Development and control of a two DOF linear–angular precision positioning stage

• A compliant mechanism capable of coupled X–θ motions is proposed.
• The input structures are computationally optimised to increase the working range.
• An adaptive sliding mode control methodology based on dynamic modelling is proposed.
• Experimentation is performed to verify the 2D workspace and computational results.
• Experimental control results demonstrate nano-scale trajectory tracking.

This paper presents the mechanical design, optimisation and tracking control of a flexure-based positioning stage to generate coupled linear and angular motions. The mechanism employs two piezoelectric actuators, with output translation and rotation proportional to the difference and sum of the input displacements. Computational optimisation utilising finite element analysis is used to develop designs that maximise the working range. A dynamic model is developed, leading to the establishment of a proposed sliding mode controller to allow the stage to track desired trajectories. An adaptive gain is implemented to reduce errors in the estimated kinematics, and accommodate creep within the mechanism. A prototype of the mechanism has been manufactured, and experimentation has been performed to verify computational predictions of the mechanism behaviour. The ability of the proposed controller to execute precise tracking of a desired trajectory within the workspace is demonstrated in the experimental study.