Determining the uncertainty of the object coordinate system position coordinate measurements of free-form surfaces

Coordinate measurements are a source of digital data in the form of coordinates of measurement points with a discrete distribution on the measured surface. Geometric deviations of free-form surfaces are determined at each point as nor- mal deviations of these points from the nominal surface (a CAD model). The calculations are preceded by fitting the measurement data to the CAD model. The relations between the object coordinate system and the coordinate system of the machine are described by the transformation parameters. This paper presents the idea of the process of data fitting with the use of the least square algorithm method as well as the way of determining the uncertainty on the assumption that transformation para- meters are subject to a multivariate normal probability distribution. The theoretical issues were verified by experiments carried out on a free-form surface obtained in the milling process and characterised by random geometric deviations.