Abstract: To assure accurate measurement of irregularities of the geometrical surface structure, it is necessary to mathematically define a relevant reference surface (an associated surface, according to the latest terminology). This surface is the reference feature in relation to which appropriate parameters are calculated. Cylindricity deviations are generally evaluated using least squares or minimum zone cylinders as the associated features. Elements that are not nominally cylindrical, for instance, barrel- or saddle-shaped, cannot be measured applying an ideal cylinder as the associated feature. This paper presents a mathematical model for the calculation of the associated feature for barrel- and saddle-shaped elements whose generatrices constitute the circular segments, and the results of the experimental verification of the proposed concept. The basic assumptions of the concept are that measurements are conducted using the radial method, and that the specially developed software can be used for accurate measurement of elements with considerable changes in diameter.
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