## 2 Checking the Geometry and Shape of the Assessed Car Roof
### Laser Tracker Systems  
The optical laser method called laser tracker systems is currently a standard part component of automated lines, especially in automotive plants. It is one of the most accurate and fastest methods for analyzing the unevenness of complex components. Scanning 3D objects is used, for example, to check tolerances of individual dimensions in real time. The measuring set used consists of a static part of the Leica Absolute Tracker AT960 and a portable Leica T-Scan 5 [12]. The apparatus enables data collection at a speed of up to 160 lines per second, or up to 210,000 points per second. The identification of the position in space is realized on the basis of reflection of the laser beam from the optical system of mirrors, which are distributed around the entire circumference. The greatest advantage is the possibility to measure various types of surfaces--from matt to reflective. The computer software then evaluates measured data and, by comparing them with model values, deviations are determined at analyzed points. The accuracy of the equipment specified by the manufacturer is \(\pm\)60 \(\upmu\)m to a distance of 8.5 m.  
The main advantage of the device is not only the compact character and easy operation, but the possibility to validate measured dimensions of the real product with a software 3D model at predetermined points. Figure 4 shows a process of measuring displacement of the analyzed roof before mounting the antenna. Figure 5 shows the measured fields of roof displacement before and after mounting the antenna. The displacement measurement points were selected so that it was possible to compare the change near the hole (points 1 to 20) but also in the vicinity of the antenna cover (points 21 to 38). Figure 4: Displacement measurement with the Leica T-Scan 5 around the hole before mounting the antenna. Figure 3: Light reflection test after mounting the antenna. Table 1 compares displacement values at selected locations according to Figure 5. In the case of measurement after installation, the area under the antenna cover was not evaluated (stage 3). Places where displacements have not been evaluated (measured) are marked in gray. Deviations of values between individual stages are given in Table 2. Three stages were analyzed. The first stage was represented by deviations of displacements after the application of strain gauges to the unloaded roof (2/1). The second stage was the comparison of the displacement after the antenna  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Measuring Place**} & \multicolumn{3}{c}{**Displacement (mm)**} & \multirow{2}{*}{**Measuring Place**} & \multicolumn{3}{c}{**Displacement (mm)**} \\ \cline{2-9}  & **Stage 1** & **Stage 2** & **Stage 3** & **Stage 4** & **Stage 1** & **Stage 2** & **Stage 3** & **Stage 4** \\ \hline
1 & 0.75 & 0.72 & - & 0.74 & 21 & 0.55 & 0.54  
mounting with the state after application of strain gauges (3/2). At this stage, it was not possible to evaluate deviations at locations 1 to 20. The last step was to compare values of displacements after disassembly of the antenna against the state after application of sensors--i.e., with the conditions before antenna mounting (4/2). An interesting fact was the finding of deviations in the same operation in both directions. The most important fact is that significant deviations occurred after the installation of the antenna in places 34 to 36, where the difference in values reached almost 47% (in absolute terms, the difference equals 0.3 mm). Nevertheless, this condition is not critical for the assessment of car operation safety, but these deviations may already be visible to the eye. For easier interpretation of numerical values given in Table 1, a displacement filed can be used (Figure 5). From the asymmetrical distribution of the displacement fields, it is clear that the deformation of the sheet metal registered before the actual assembly of the antenna is different on the right and left side.