## 3 Results and Discussion
As in the case of normal movements, the duration of the steady phase in fast movements decreases as the range of movement decreases. For the C\({}_{1}\) movement range, the duration of the steady phase constitutes 5-8% of the total movement, while for the C\({}_{3}\) movement range, it constitutes 2-4% of the total movement. Based on the obtained research results and Equations (7)-(11), the individual power and energy requirements of manipulators with different ranges, performing movements in the operating ranges C\({}_{1}\), C\({}_{2}\), and C\({}_{3}\), were determined. The summary of the obtained power indices \(N_{amax}^{*}\) and \(N_{dmax}^{*}\) for the tested size ratios, ranges, and types of movement is presented in Figures 15-17. Analyzing the presented graphs, it can be seen that the value of the power index in fast movements is from 3 (for K = 2.5) to 6 times (for K = 10) higher than in normal movements. The difference in power meter values between fast and normal movements will compound as the size ratio value and move range decrease. For example, the power index for K = 10 and the C\({}_{1}\) range is 60% greater than the power index for K = 2.5 and the corresponding range of motion. In the case of fast movements, the difference in power indicators is much greater, and when comparing the value of the power indicator for K =  
Comparing the power index for the acceleration and deceleration phases, it can be noticed that for both fast and normal movements, it has lower values for the deceleration phase. The difference in the case of normal movements ranges from 20 to 28% and is the smallest for movements with the smallest C\({}_{3}\) range. In the case of fast movements, the difference is greater and amounts to up to 70%. In the case of fast movements, the greatest differences can be observed for movements with the smallest reinforcements and the smallest ranges, unlike in the case of normal movements. A significant value of the power indicator occurring in the braking phase, regardless of the movement, indicates the validity of attempting to recover energy, store it, and use it to implement the acceleration phase when operating manipulators. The list of energy indicators, calculated in accordance with Equations (9)-(11), in the acceleration phase--\(E_{\text{fl}}^{*}\)--steady phase--\(E_{\text{ks}}^{*}\)--and deceleration phase--\(E_{\text{kd}}^{*}\)--for the tested size ratios, ranges, and types of movement is presented in Figures 18 and 19. Figure 16: Summary of the power index obtained from the tests for the ranges of motion and size ratio K = 5. Figure 17: Summary of the power index obtained from the tests for the ranges of motion and size ratio K = 2.5. Regarding the analysis of changes in the energy index value, a similar trend of changes in the power index can be observed. The highest values of the energy index occurred for the highest values of size ratios and ranges of motion in both normal and fast movements. The maximum values of the energy index reached 0.08 m\({}^{2}\)/s\({}^{2}\) for the longest ranges of C\({}_{1}\) movement and size ratio K = 10 in fast movements and were almost four times higher than in the case of the analogous parameters in normal movements. The energy index in the steady phase (PS) constitutes from 12 to 15% of the total energy index in normal movements, and in fast movements, it constitutes from 13 to 19% of the total index.