The improved reversal method for measurement of geometric error in linear manipulator of ultra precision

In this paper, novel reversal method is proposed to estimate the straightness errors (horizontal/vertical) and angular errors (pitch/yaw) of a linear axis using two capacitive sensors and a measurement target. These errors are estimated using the data of capacitive sensors including the standard uncertainty of sensors, itself. So the standard uncertainty of sensors would adversely affect the standard uncertainty of estimated geometric errors. It is affected by the relative position between reference coordinate system and sensors because of Abbe's error. To solve this problem, proposed reversal method optimizes the relative position between reference coordinate system and sensors for minimum standard uncertainty of estimated geometric errors. The estimated geometric errors using proposed method is compared with the measured data using the laser interferometer. In the difference of these data, the maximum deviations of straightness errors are within 1 micrometer, 1.5 the arcsec for angular errors respectively. This difference value is resolution level of machine tool used at experiment, so the proposed reversal method reveals the validity.