Inverse kinematic modeling of a coupled flexure hinge mechanism

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An inverse kinematic model of a micro-motion stage with three degrees-of-freedom motion is presented. The XYθ stage uses three piezoelectric actuators and a monolithic flexure hinge mechanism which is designed to provide large θ motion. The stage design has a coupled hinge mechanism which causes a difficulty in motion control. This paper describes a computer based inverse kinematic model of hinge mechanism and the experimental verification for the model. In particular, it presents a kinematic calibration procedure for improving the accuracy of the model. It is shown that the simulation and experimental results are very similar to each other and they also demonstrate that the inverse kinematic model can be used for open loop control of the stage within 5% error. The open loop control of the stage provides 7.6 and 8.2 nm positioning resolution over the total range of 41.5 and 47.8 μm along the X- and Y-axis, respectively, and 0.057 arcsec rotational resolution over the total range of 322.8 arcsec about the θ-axis.

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