## 3 Results and Discussions
### Random Distribution of Measurement Points  
The next stage of the research involved obtaining results (Figures 6-8) based on a smaller number of measurement points.  
Figure 6: Summary of flatness error results for the automatic measuring machine with random distribution of measurement points [own elaboration].  
In the first part of the study 20, 40, 60, 80, 100, 120, 140, and 160 measurement points were selected randomly from the obtained results. In the study, \"random selection\" refers to the random selection of measurement points on the surface, without favoring specific areas. These points were chosen using appropriate random sampling techniques with a uniform distribution to avoid introducing biases stemming from prior knowledge of the surface structure. Such a methodology allows for the collection of representative data, enabling an objective assessment of flatness. Due to the expected lack of repeatability of the flatness result obtained in this manner, each test was performed three times. This means that each time, points were selected from different data sets, and the measurement was also performed three times.  
Figure 8: Summary of flatness error results for the measuring arm with random distribution of measurement points [own elaboration].  
Figure 7: Summary of flatness error results for the manual measuring machine with random distribution of measurement points [own elaboration].  
Random selection of measurement points on the deformed surface of the plate shows underestimated flatness error values for 20-40 points, which is evident in Figure 6. For measurements above 80 points, the change in the obtained results is minimal and is less than 10 \(\upmu\)m.  
In the case of results from a manual machine, Figure 7 presents the recorded difference in the obtained results even for 80 points. When measuring above 100 points, the discrepancy of the obtained results falls below 10 \(\upmu\)m and is close to the values obtained from an automatic machine.  
Measurements obtained in the range up to 100 points show both a large diversity and a deviation from the average value of the total number of measurements, which can be observed in Figure 8. For a greater number of measurement points, the deviation also stabilizes within an error margin of \(\pm\)10 \(\upmu\)m; however, the average value is about 10 \(\upmu\)m higher.  
Based on the obtained results, a summary was prepared of the time needed to conduct the study and the observed deviation, as the average result from the three quantities of collected points obtained in the study--Figure 9.  
The time it takes to perform measurements for an automatic machine is significantly longer than for the other two devices. This especially pertains to the time needed to prepare the device before starting the measurements. The measurements can be started fastest on a manual machine; however, in the case of measuring a larger number of points (according to the chart, about 180 points), the total measurement time for an articulating measuring arm is shorter.  
The flatness error obtained from the articulating measuring arm is larger than in the manual machine, but the error range for the obtained results is smaller. In the case of the automatic machine, the measurement results for both the average value of the error and the error range are the smallest.