Tschebyscheff approximation for the calculation of maximum inscribed/minimum circumscribed geometry elements and form deviations

The calculation of dimensional deviations is mandatory for the quality inspection of geometry elements. This paper describes a method for the approximation of geometry elements by Gauss/Tschebyscheff algorithms. Moreover, the Tschebyscheff algorithm is the correct approach to determine correctly standardized form tolerances like roundness, flatness or cylindricity deviations. A modification of the conventional Tschebyscheff algorithm leads to maximum inscribed and minimum circumscribed elements. The presented Tschebyscheff algorithms are applied to circles, cylinders and other geometry elements and verified by using test profiles.