## 4 Measured Data
### Measured Data--Link 2  
Figure 8 shows four boxplots for link 2 (when viewed from left to right for an initial joint angle of 10\({}^{\circ}\) to 40\({}^{\circ}\)). In these graphs, in comparison with the graphs for link 1, it can be seen that the minimum and maximum values of the set initial angles are much further apart, which results in a more significant shift of the mean value from the desired initial angle (especially for the angle \(-40^{\circ}\), fourth graph from the left). The remote value was measured only for an angle of 20\({}^{\circ}\) (red crosses, second graph from the left), two times (\(-17.28^{\circ}\) and \(-14.832^{\circ}\)). Figure 8: The boxplots of initial values of joint angles—link 2. Figure 7: The mean response and standard deviation for the joint angle 40\({}^{\circ}\)—link 1. While for link 1, the initial angles were set in the range of up to \(1^{\circ}\), the setting of the initial joint angle for the measurements of link 2 was more difficult in terms of constraints in the construction of the system. Figure 9 graphically presents the mean response (red curve) and standard deviation (grey area) when the initial angle was set to \(-10^{\circ}\). The total interval of the initial values of the angle of rotation was \(<\)\(-7.92^{\circ}\); \(-10.08^{\circ}\)\(>\), the Mode from the twenty initially set angles was \(-8.928^{\circ}\). As the joint angle for link 2 increases, the range of the intervals of the initial values of the joint angle also increases (it is also visible in the area of the standard deviation parameter in Figure 10). The interval for the initial value of the joint rotation angle \(-20^{\circ}\) is \(<\)\(-14.832^{\circ}\); \(-21.888^{\circ}\)\(>\), where the difference between the minimum and maximum value of the interval already exceeds \(7^{\circ}\). Nevertheless, the value of the Mode parameter (\(-20.736^{\circ}\)) is close to the reference value. The interval for the reference value \(-30^{\circ}\) for link 2 was \(<\)\(-23.904^{\circ}\); \(-31.248^{\circ}\)\(>\), where from the range of initial values, it is possible to monitor a more significant value of the parameter Mode (\(-24.048^{\circ}\)) in comparison with the reference value. The shift of the beginning of the mean response curve (Figure 11) and the standard deviation area itself is caused by one of the measurements when the initially set value was \(-23.904^{\circ}\). Figure 10: The mean response and standard deviation for the joint angle \(20^{\circ}\)—link 2. Figure 9: The mean response and standard deviation for the joint angle \(10^{\circ}\)—link 2. The last measured data was for the initial joint angle was \(-40^{\circ}\). The total interval of the initial values of the joint angle was \(<\!-32.976^{\circ}\); \(-42.192^{\circ}\)\(>\), the Mode of these twenty values was \(-38.736^{\circ}\). In Figure 12, it is possible to see the fact that the variance in the measurements is the most expressive, which of course, was reflected in the standard deviation. Gravity tests showed that within link 1, the time course of mean response of the joint angle was more uniform with gradual stabilization to the value of the zero joint angle. For link 2, it is clear from the graphic waveforms that the course is different compared to link 1. A more pronounced stabilization for link 2 for each initial joint angle begins only after a certain amplitude has been exceeded. Additionally, in the case of graphical dependencies, link 2 can see more significant friction, which can affect the validation process. Further, from the sample mean responses and standard deviations for link 1 and link 2, it can be presented that for initial joint angles of \(10^{\circ}\) and \(20^{\circ}\), the standard deviation range is narrower than for \(30^{\circ}\) and \(40^{\circ}\) for both axes, which means that at higher initial joint angles, the deviation from the mean response is more pronounced.