## 2 Materials and Methods
### Experimental Setting and User Task  
In order to determine the speed of the effector, a lab stand was built in which the movement of the effector (slave) was simulated by the movement of the laser spot on the screen. The operator's task was to move the spot between the markers by hand-moving the lever with the laser pointer (Figure 1) which was imitating the master controller.  
Each subject moved, using his hand, the laser spot (effector) displayed on the screen from point A to B (right to left) and back from B to A (left to right) in a straight line.  
Changing the operator's distance from the screen made it possible to change the size ratio. Horizontal, lateral movement of the operator's hand was about 800 mm and was in the comfort zone according to [38]. During hand movement viewing angle was about \(\alpha_{\mathrm{v}}=60^{\circ}\), for which human is capable of recognizing colors [39]. The research was conducted for distances 2, 4, and 8 m, which gave size ratio \(K=2.5\); \(K=5\) and \(K=10\). These are typical size ratios during positional control for manipulators with a large working area [23; 24; 31; 40; 41; 42; 43].  
In the first stage, the subjects performed manipulative tasks at a velocity they considered normal-normal movements. In the second stage, the subjects performed the tasks with the maximum velocity possible for them--fast movements. Normal movements were defined as those that allow the hand to be moved at a subjective velocity that ensures stable hand guidance during the performance of a defined task. Fast movement is considered to be one in which the hand is moved at a velocity that ensures the fastest possible execution of the task.  
All subjects performed normal and fast movements with their dominant hand. Each subject performed trials with six normal and six fast movements for each. Therefore, the number of recorded, normal movements was 540 (30 subjects \(\times\) 6 movements \(\times\) 1 direction \(\times\) 3 size ratio) and for fast movements was the same number of records 540 (30 subjects \(\times\) 6 movements \(\times\) 1 direction \(\times\) 3 size ratio). This test was measured after two practice trials.  
According to [31], during the realization of human hand movements the acceleration phase (p\({}_{\text{a}}\)), the steady motion phase (p\({}_{\text{s}}\)), and the deacceleration phase (p\({}_{\text{d}}\)) can be observed. Therefore, the following indicators were adopted to evaluate the research results (Figure 2):  
* the maximum velocity of the operator's hand movement for all size ratios from the entire range for normal and fast movement--\(V_{MAX}\),
* the average effective velocity of the operator's hand movement for all size ratios for the steady motion phase for normal and fast movement--\(V_{S}\);
* the average value of acceleration phase time duration (p\({}_{\text{a}}\)) for all size ratios from the entire range for normal and fast movement--\(t_{a}\);
* the average value of steady motion phase time duration (p\({}_{\text{s}}\)) for all size ratios from the entire range for normal and fast movement--\(t_{s}\);
* the average value of deacceleration phase time duration (p\({}_{\text{d}}\)) for all size ratios from the entire range for normal and fast movement--\(t_{d}\).  
Figure 1: Scheme showing the idea of research on the impact of size ratio on the velocity of the operator’s hand movement, described in the main text.  
The steady motion phase (p\({}_{\rm{s}}\)) is the phase during which the velocity of the operator's hand movement does not change more than 5%.