## 3 Results and Discussions  
To unambiguously and mathematically determine the position of the studied plane in space, it is necessary to collect a specific number of points. For a plane, three points are needed, while for a line, two are needed. To increase the accuracy of the measurement, a larger number of points were collected. Faro's training materials recommend collecting seven points for a plane and five points for a line [22]. The distribution of points collected during the examination of the element is shown in the figure below (Figure 4). In order to conduct a comparison of the three selected measuring devices, a measurement of the surface of the element was performed at regularly spaced points. To increase the accuracy of the obtained results, 189 evenly distributed measuring points were collected from the tested surface for each of the examined methods. Figure 4: Diagram for determining the position of the tested element in the measuring space of the machine [own elaboration]. Since the parameters of the measuring probes, the diameters of their balls, and especially the length are important factors affecting the accuracy of the measurement, a system with the same parameters was used for all studies [19]. Automatic measuring machine. Both automatic and manual measuring machines are equipped with contact, trigger probe heads. These are heads commonly used in coordinate-measuring machines. Thanks to their high precision and sensitivity of the probes, as well as the use of modern algorithms for correcting the radius of the measuring tip, they demonstrate high reliability of the positioning of the obtained results in the measuring space [23]. Preparing an automatic measuring machine requires not only startup and calibration but also writing a measurement program. Due to the weight of the part and the low pressure of the measuring probe, as well as the automatic operation that eliminates the accidental displacement of the element, there is no need to mount it. The measurement program required determining the position of the examined element in the measuring space of the device each time. After completing the measurement, an automatic file with the obtained measurement data was created--Figure 5a. Characteristic parameters:  
Time needed to prepare the device: 4 min;  
Time to write the measurement program: 16 min;  
Measurement time of the plate: 12 min;  
Total research time amounted to 32 min. The measurement data presented in Figure 5a indicate the bulging of the central part of the tested sample along the X-axis. Furthermore, there is visible twisting of the transverse section of the tested element. The surface of the chart is gently deformed and is contained between the Z-axis values of \(-20\)\(\upmu\)m and \(30\)\(\upmu\)m.  
Manual measuring machine. After starting the manual measuring machine and conducting the calibration of the measuring probe, a coordinate system was described on the part mounted on the machine. The next step was to perform four measurements at designated points on the surface of the element. An auxiliary grid applied to the plane was used to determine the examined point on the surface of the plate. After conducting the study, the obtained results were saved as a file with data containing three coordinates of the measured points--Figure 5b. Characteristic parameters:  
Time needed to prepare the device: 6 min;  
Measurement time of the plate: 13.5 min;  
Total research time amounted to 19.5 min. Figure 5: Measurement data obtained during measurement with [own elaboration]: (**a**) an automatic measuring machine (dimensional deviations); (**b**) a manual measuring machine (dimensional deviations); (**c**) the measuring arm (dimensional deviations). The values plotted in Figure 5b indicate bulging and twisting of the tested sample. The mapped surface is more gentle and falls within the range for the \(Z\)-axis from \(-20\)\(\upmu\)m to \(40\)\(\upmu\)m.  
Measuring arm.