A mobile multilateration measurement system developed at the Physikalisch-Technische Bundesanstalt (PTB) around 2010 has been thoroughly investigated and refined to gain better performance with smaller uncertainties even when applied to the calibration of large complex workpieces. The mathematical background of multilateration and the propagation of uncertainties for the algorithms involved is explained in detail. Using the example of simple 1D and 2D measuring tasks, the influence of certain parameters characterizing the setup of the measurement system on the overall uncertainty is quantified. A strategy is developed to incorporate multi-stylus measurements which are often inevitable when workpieces feature complex shapes. The findings are verified on a large involute gear which is 2 m in diameter. All measurements are performed on PTB’s large coordinate measuring machine with a working range of 5 m × 4 m × 2 m .

We propose a unified theory for the metrological treatment of helical machine elements such as cylindrical and conical gears, worms, and screw threads. The main idea is to introduce a universal 3D geometry model for threaded components that provides for distinct parameterization using a unique set of geometry parameters and that offers and a functional description of the transverse profile. Using modern 3D coordinate measuring technology, a holistic evaluation algorithm yields the actual geometry as the result of a high dimensional best-fit procedure and form deviations as corresponding residuals. All determinants and evaluation parameters can then be calculated from the set of actual geometry parameters. By applying certain constraints to the model to be fitted, the novel method can be reduced to the established 2D methods and hence meets demands for the comparison of the two procedures. The results of the novel approach have proven to be very stable and they enable the evaluation of areal measurements with no loss of information.

A novel method for the determination of rotary table errors with six degrees of freedom on coordinate measuring machines and machine tools is introduced. The method is based on the measurement of an uncalibrated circular ball plate in different rotational positions on the rotary table, which is also referred to as the three-rosette method. The novel procedure allows the number of measurement positions to be reduced significantly compared to the complete three-rosette method, while the measurement uncertainty still remains sufficiently small. The method relies on error separation and is self-calibrating, which means that no external reference is required. The sophisticated design of a new ball plate allows rotary table errors to be determined in angular steps of only 5^∘.

The three-rosette method is a well-established self-calibrating error-separation method used for highly accurate pitch calibrations of cylindrical gears on coordinate measuring machines or gear measuring machines. It is based on the principle of circle closure and uses multiple measurements in different relative positions of the gear with respect to the measuring device. However, since its measurement effort is proportional to the square of the number of teeth, the method is of limited usability for gears with a large number of teeth. In this paper, a reduced method which requires much fewer measurements is described. This method is based on the same error model and is still self-calibrating. The measurement uncertainties for this method are only slightly higher than for the complete method. After an introduction to the three-rosette method, this paper describes the impact of the number and choice of the measured relative positions on the measurement uncertainty. Moreover, the problem of an erroneously determined gear axis is addressed. Finally, the effectiveness of the reduced three-rosette method is shown in intercomparison measurements with four participants. The obtained E _n scores show that the reduced three-rosette method allows pitch calibrations with nearly the same accuracy as can be achieved with the complete method. The reduced three-rosette method is part of the TraCIM online service ( https://tracim.ptb.de ) of the Physikalisch-Technische Bundesanstalt (PTB) allowing software manufacturers or calibration laboratories to obtain a certificate for their algorithms of the reduced three-rosette method after a successfully performed software test. Moreover, calibration laboratories can receive accreditation by the German national accreditation body (DAkkS) for pitch calibrations performed by using the reduced three-rosette method.