Laser vector measurement technique for the determination and compensation of volumetric positioning errors. Part I: Basic theory

A new laser vector method for the measurement of the volumetric positioning errors of a computer numerically controlled machine or a precision instrument is described here. Compared with conventional laser interferometer measurement, the laser vector method measures the vector errors, namely, the displacement error, vertical straightness error, and horizontal straightness error, rather than the displacement error only. The key to the laser vector method is that the measurement direction or the laser beam direction is not parallel to the displacement direction. With four setups, all three displacement, six straightness, and three squareness errors can be determined. Once the volumetric positioning errors are measured, they can be used to compensate for the repeatable positioning errors of the machine or instrument. The basic concept, theory, and measurement errors are described. Experimental verification of the vector method is in the Part II of this article.