## 3 Results
### Results of Research on Reaching Movements  
Exemplary waveforms of changes in speed and acceleration for one of the operators obtained as a result of the study of the hand reaching movements depending on the direction of movement performed are shown in Figures 5-7. Figure 5: An example course of changes in displacement, velocity, and acceleration for the vertical hand movement (displacement: 930 mm), where p is the phase of the movement. Analyzing the presented waveforms (Figures 5-7), two stages of movement can be distinguished. The first is related to the movement to achieve the goal (point B in Figure 2); the other is for getting back to the starting position (point A). At each stage of movement, one can observe: an acceleration phase--PAkl, a steady motion phase--PSkl, and a deceleration phase--PDkl, where l refers to the type of movement (longitudinal--x, lateral--y, and vertical--z), and k designates the movement (l--motion to achieve the target, 2--return movement). The steady motion phase is considered a period when the speed does not change by more than 5%. It should be noted that, with the shortening of the length of motion, the steady state phase decreases. For small displacements, it may disappear. The values of the duration of the first (movement to the target) and second stage (return movement) of the hand movement during the tests for all operators are summarized in Figure 8. A box plot to show the distribution of the dataset was used. In a box plot, numerical data are divided into quartiles, and a box is drawn between the first and third quartiles, with an additional line drawn along the second quartile to mark the median. The minima and maxima outside the first and third quartiles are depicted with lines, which are often called whiskers. The mean value is marked by an x. They show that the average time for the return movement is usually longer--differences amounted to 9% for lateral movement, 10% for longitudinal movement, and 20% for vertical movement. The ANOVA F [101] analysis showed that there are no significant differences between the time of movement to the target and the time of return for longitudinal movement (F (1.238) = 3.469, \(p\) = 0.07) and lateral movement (F (1.238) = 2.43, \(p\) = 0.12). For the vertical motion, F (1.238) = 19.32 and \(p\) < 0.05, indicating the significance of the difference between the time of movement to the target time and the return movement of large displacement. Figure 6: An example of the course of changes in displacement, velocity, and acceleration for the lateral movement of the hand (displacement: 730 mm), where p is the phase of the movement. Figure 7: An example of the course of changes in displacement, velocity, and acceleration for the hand longitudinal movement (displacement: 430 mm), where p is the phase of the movement. The summary of the recorded values of the maximal speed of movement and the effective RMS (Root Mean Square) speed obtained during the study of reaching hand movements in the acceleration phase and the deceleration phase is shown in Figures 9-12. Figure 8: Duration of the individual stages of the movement, obtained during the study of the reaching movements of the hand. Figure 10: Summary of RMS velocity values obtained in the study of reaching movements in the acceleration phase. Figure 9: Summary of the maximal velocity values obtained in the study of reaching movements in the acceleration phase. Figure 16: Summary of rms acceleration values obtained in the study of reaching movements in the deceleration phase. Figure 14: Summary of rms acceleration values obtained in the study of reaching movements in the acceleration phase. Figure 15: Summary of the values of maximal accelerations obtained in the study of reaching movements in the deceleration phase. Analyzing the graphs (Figures 9-12), it can be noticed that the average maximal values of the hand movement speed towards the target (point B) were at the level of 1.01-1.13 m/s, while the average maximal speeds of the return movement were slightly lower at 0.93-1.05 m/s.