Modeling and analysis of laser shaft alignment using 4 × 4 homogeneous coordinate transformation matrix

Abstract

The current study constructs a measurement system comprising a laser light source and a detector to facilitate the alignment of two rotating shafts. The alignment process is modeled and analyzed using a 4 × 4 homogeneous transformation matrix. The analysis commences by using the transformation matrix to trace the paths followed by the skew rays within the alignment system. Analytical formulae are then derived to enable the major misalignment parameters of the two shafts, namely the horizontal angularity, the horizontal offset, the vertical angularity and the vertical offset, to be inversely extracted from the detector readings such that the two shafts can be correctly aligned. The validity of the proposed approach is confirmed by performing a series of experimental alignment trials for various initial misalignment conditions.