Development of compact three-degrees-of-freedom compensation system for geometric errors of an ultra-precision linear axis

We report a compensation system for geometric errors of a linear axis to achieve the ultra-precision positioning. The system was miniaturized by integrating the drive and measuring components. A novel joint with three DOFs based on a flexure hinge was developed to obtain the ultra-precision positioning. The drive component, which was adapted to the parallel mechanism, had a high structural stiffness and rapid response characteristics. The rotational stiffness of the joint was calculated and the mode shapes were analyzed to verify the feasibility of three-DOF motion. The measurement component consisted of capacitive sensors and a reference mirror to measure the three geometric errors of the linear axis. In addition, the optimal position between the reference coordinate system and a sensor was determined to minimize the standard uncertainties of the measured errors. The compensation system was fabricated and evaluated experimentally. A compensation algorithm based on a recursive technique was developed to improve the positioning accuracy of the system. The geometric errors of the linear axis were measured and compensated for, and a marked improvement was observed compared to the case with no error compensation. The peak-to-valley error of the translational and rotational errors were reduced by 92% and 98%, respectively.