## 3 Results  
The Shapiro-Wilk test was used to check the normality of the distribution. The significance level \(\alpha=0.05\) was adopted. For 30 people tested according to the data in the tables of coefficients for the Shapiro-Wilk test [47], the critical value is \(W_{(0.05,30)}=0.927\). The normality of the RMS velocity distribution for fast and normal movements was checked for size ratio \(K=2.5\), \(K=5\), \(K=10\). The following results were obtained:  
* fast movements:
* for \(K=10\): W = 0.947; \(p=0.144\);
* for \(K=5\); W = 0.952; \(p=0.201\);
* for \(K=2.5\); W = 0.964; \(p=0.390\);
* normal movements:
* for \(K=10\); W = 0.938; \(p=0.181\);
* for \(K=5\); W = 0.957; \(p=0.269\);
* for \(K=2.5\); W = 0.964; \(p=0.406\). The obtained results of the Shapiro-Wilk test indicate that the distribution of the obtained test results is close to normal. Power analysis of the ANOVA test performed for normal movements (\(\alpha=0.05\) and RMSSE (Root Mean Square Standardized Effect) equal 0.9273), and fast (\(\alpha=0.05\) and \(RMSSE=0.6031\)), showed that the number of trialsis sufficient to show the difference between the velocity of movement of the effector (E) and the operator's hand (H) depending on the size ratio (\(K\)) and ensure the test power of 80%. The number of trials is also sufficient (test power over 80%) necessary to show the differences between the velocity of movement depending on its direction (from A to B or from B to A) for different size ratio of normal movements (ANOVA for \(\alpha=0.05\); RMSSE = 0.8509) and fast (ANOVA for \(\alpha=0.05\); \(RMSSE=0.5857\)). Example waveforms of velocity changes for one of the operators obtained as a result of research for normal and fast movements of the operator's hand for three size ratio values are shown in Figures 6 and 7. (1--from A to B, 2--from B to A), \"?\" indicates the type of movement performed (N--normal movement and F--fast movement) and \"\(K\)\" is the size ratio. Note that as the size ratio value decreases and the movement velocity increases the steady motion phase decreases. For fast, low-size ratio movements, it may fade away. In order to check whether there are significant differences in the velocity of movements depending on the turn (movement from A to B compared with B to A), ANOVA F analysis was performed for the analyzed reinforcements and types of movement. The analysis showed that the direction of movement does not significantly affect the RMS velocity. In the case of ANOVA F for the RMS velocity in normal movements obtained:  
* for \(K\) = 10--F (1,118) = 0.256, \(p\) = 0.626,
* for \(K\) = 5--F (1,118) = 0.011, \(p\) = 0.916,
* for \(K\) = 2.5--F (1,118) = 0.050, \(p\) = 0.828. ANOVA F for the RMS velocity in fast movements showed:  
* for \(K\) = 10--F (1,118) = 0.319, \(p\) = 0.587,
* for \(K\) = 5--F (1,118) = 1.444, \(p\) = 0.315,
* for \(K\) = 2.5--F (1,118) = 1.277, \(p\) = 0.291. Due to the lack of significant differences between the RMS velocity values of the movements depending on the turn, the analysis of the significance of changes in the remaining parameters was omitted. The entire movement was subjected to further analysis, averaging the achieved velocity of movements. A summary of the time duration of the acceleration phase--t\({}_{\text{a}}\), steady motion phase--t\({}_{\text{s}}\), and the deceleration phase--t\({}_{\text{d}}\), depending on the scale ratio--\(K\), is presented in Figure 8.  
Based on the presented graph (Figure 8), it can be concluded that the deacceleration phase (p\({}_{\text{d}}\)) has the largest share in all completed movements. Its duration is 2.2 s for normal movement with \(K\) = 10 and 1 s for fast movement with \(K\) = 2.5. The steady motion phase duration (p\({}_{\text{s}}\)) decreases as the size ratio decreases.