Analysis and On-Machine Measurement of Full-Field Cross-Talks of Stacked X–Y Stages

Abstract Geometric errors are inherent in any moving stage. Usually, they are considered position-dependent on their own axis. Herein, a unique structural-analysis framework is designed to investigate mutual quasistatic cross-talks between stacked X and Y axes. The method reveals the manners in which (1) the upper-stage mass induces angular errors in the lower stage and (2) the lower-stage angular deviations cause angular responses in the upper stage. To achieve the full-field observation of these coupling behaviors, an on-machine, embedded, five-degree-of-freedom sensor module is designed for the simultaneous measurement of two straightness errors and three angular errors along multiline paths. Experimental verification demonstrates remarkable repeatability, stability, and strong consistency with analytical predictions. The results confirm that the position-dependent geometric errors of X–Y planar stages should be modeled as two-dimensional functions for achieving accurate error calibration and compensation. The proposed method provides a compact, full-field, practical solution for analyzing and increasing the accuracy of multi-axis motion systems.