## 2 Methods
### Experimental Setting and User Task  
The tests were carried out on the test stand shown in Figure 1. The station allows us to simulate the movement of the manipulator effector in the form of a laser spot in proportion to the movement of the operator's hand. The research consisted of moving the laser spot on the screen between vertical markers (A, B) by the operator moving the lever on section A'B', to which the laser pointer was attached (which simulated the primary controller). Each operator had to move the laser spot from A to B and back along a straight line. Because previous research [11] showed that the velocity of effector movement does not depend on the direction of the straight-line trajectory, the research was carried out only in the field of lateral movement. Depending on the distance L of the operator from the screen (corresponding to the range of the manipulator), it was possible to simulate the movement of the manipulator effector with a different working area (characterized by different kinematic amplifications). Due to the typical ranges of manipulators with a large working area [1, 11, 21, 33, 34], the tests were carried out for three ranges L (6 m, 3 m, and 1.5 m), corresponding to the size ratio K of \(\times\)10, \(\times\)5, and \(\times\)2.5. The maximum marker spacing (effector movement range) was 8 m, 4 m, and 2 m, respectively. The range of motion of the effector was within the human color vision zone, which is approximately 60-70\({}^{\circ}\) and within the human stereoscopic field of vision, which is approximately 100-120\({}^{\circ}\)[35, 36, 37]. Additionally, to improve perception, operators could move their eyes or head. The hand displacement that was necessary to induce such a movement was C\({}_{1}\) = 0.8 m and was within the operator's comfort zone in accordance with the requirements contained in [38, 39, 40]. In order to check the influence of the effector's range of motion on the velocities, accelerations, and power and energy demand, additional tests were carried out, reducing the marker spacing by 50% and 75%, which corresponded to the hand movement at C\({}_{2}\) = 0.4 m and C\({}_{3}\) = 0.2 m. Table 1 lists the ranges of movements that were performed by the operator and the effector for the tested manipulator's size ratios and ranges. The tests were carried out for two velocities of movement of the manipulator effector: normal and fast movements [11]. Normal movements did not require special focus and maximum attention from the operator, while fast movements corresponded to the velocity at which the operator was able to perform the given task as quickly as possible. Effector velocities and accelerations were determined based on hand movement measurements using the size ratio used. Three phases were distinguished in the analyzed movements: acceleration (\(t_{a}\)), steady movement (\(t_{s}\)), and braking (\(t_{d}\)) (Figure 2). The time in which the movement velocity does not differ by more than 5% from the maximum value was considered to be a steady phase. Based on the recorded data, the following were determined:  
* \(v_{s}\)--the average effective velocity of the effector's movement for the entire steady motion phase (PS);
* \(a_{max}\)--the maximum acceleration of the effector's movement for the acceleration phase (PA);
* \(a_{max}\)--the maximum acceleration of the effector's movement for the deceleration phase (PD);
* \(t_{s}\)--the average steady motion phase duration;
* \(t_{a}\)--the average acceleration phase (PA) duration;
* \(t_{d}\)--the average deceleration phase (PD) duration. Based on the recorded runs, the maximum value of power indicators was determined for the following phases:  
* Acceleration phase \(N^{*}_{amax}\) according to the following equation:  
\[N^{*}_{amax}=\text{max}(v(t)\cdot a(t))\ \ \ \ \ t\in<t_{1},t_{2}> \tag{7}\]