Symmetry centering of artifacts on limited-range rotary carriages or joints

Abstract

This note describes a symmetry-based technique to center a part or artifact having a complete, partial or intermittent fiducial surface having an axis-of- revolution onto the axis-of-rotation of a rotating joint, stage, or flexure which has limited rotational travel. It is shown that using limited rotations and by sensing in the X-direction, the Y misalignment can be independently determined and/or by sensing in the Y-direction the X misalignment can be independently determined. Further if measurements are balanced using an ±ε < 40° rotations then the sensed magnitude variation is approximately ε/30° times the offset in the orthogonal direction when the joint is balanced halfway between the ±ε excursions. This may also be of use when positioning hemispheres or artifacts on rotary tables with their axis of rotation perpendicular rather than parallel to the rotary table axis. This technique also allows for adjustments during the initial alignment when the error may be greater than the working range of a probe and thus preventing a full 180° reversal for centering determination. Although it is possible to get both eccentricity components using single direction measurement it is not recommended due to much higher sensor-noise-related uncertainty.