## 3 Enhancing Movement Quality by Implementing a Compensation Function  
The experimental studies have shown the significant impact of the mass of the components in the \(\varphi_{2}\) axis on the quality of movement. In order to improve the operation of the system, this impact had to be compensated for. For this reason, special procedures were developed: analytical and experimental. Firstly, an analytical method was used to determine the torque acting on the \(\varphi_{2}\) axis. At that time, friction forces between the elements were omitted, and the method served as a verification for the experimental method. The masses and centers of masses of the individual elements were determined, and then their lever arms were calculated (Figure 10, Table 1). Figure 9: Characteristics of sinusoidal complete cycle: (a) \(\varphi_{szp2}(t)\)-input signal, \(\varphi_{2}(t)\)-measurement result, \(\omega_{2}(t)\)-angular velocity; (b) position error: \(e_{2}(t)\). The maximum analytically calculated \(\varphi_{2}\) axis load related to the gravity and mass of the elements was 14.04 Nm. This was calculated for the angular position \(\varphi_{2}\ =\ 0^{\circ}\). The second experiment consisted of determining \(\varphi_{2}\) axis load experimentally by using the drives' characteristics (characteristics of the generated torque depending on the current consumption) and measuring the current via the current sensor. The experiment began with setting the range of motion. For the research, the angular range for the \(\varphi_{2}\) axis was set to \(-60^{\circ}\leq\varphi_{2b}\leq 60^{\circ}\), where \(\varphi_{2b}\) is the examined angular position of the mechanism. The procedure's main goal was to determine the active torque (\(M_{\mathrm{k}}\) ) needed to keep the mechanism in a given angular position in the \(\varphi_{2}\) axis. The torque \(M_{\mathrm{k}}\)  was determined based on the measurement of the current consumed by the drive and its characteristics. The mechanism position changed by one degree at a time. The measurement was carried out in two opposite directions of movement for the \(\varphi_{2}\) axis, i.e., it was the torque needed to move the mechanism upwards and downwards from the stopped angular position. The difference between these two quantities defined the area where the mechanism remained motionless. The size of this area was related to the forces of static friction, motion resistance (mainly of the gear), and the mass of the mechanism's components. \begin{table}
\begin{tabular}{c c c c} \hline
**Item No.** & **Description** &
\begin{tabular}{c} **Mass \(m\)** \\ **[kg]** \\ \end{tabular} & **Lever Arm \(l\) [mm]** \\ \hline
1 &
\begin{tabular}{c} Gear wheels \\ \end{tabular} & 0.2 & 460.5 \\
2 &
\begin{tabular}{c} Gearbox for \(\varphi_{3}\) axis \\ \end{tabular} & 0.55 & 380.5 \\
3 &
\begin{tabular}{c} DC motor for \(\varphi_{3}\) axis \\ \end{tabular} & 0.76 & 297.1 \\
4 &
\begin{tabular}{c} Torque Snssor S3 \\ \end{tabular} & 0.30 & 336.5 \\
5 &
\begin{tabular}{c} Main body, transverse structural \\ element, S3 axis mounting \\ \end{tabular} & 1.04 & 250.0 \\
6 &
\begin{tabular}{c} Main body, bottom and top covers \\ \end{tabular} & 0.48 & 340.2 \\
7 &
\begin{tabular}{c} Main body, sensor side walls \\ \end{tabular} & 0.20 & 330.0 \\
8 &
\begin{tabular}{c} Main body, motor side walls \\ \end{tabular} & 0.29 & 329.2 \\
9 &
\begin{tabular}{c} Main body, arms, \(\varphi_{2}\) axis mount \\ \end{tabular} & 0.579 & 120.0 \\
10 &
\begin{tabular}{c} Gearbox for \(\varphi_{2}\) axis \\ \end{tabular} & 0.71 & 4.70 \\
11 &
\begin{tabular}{c} DC motor for \(\varphi_{2}\) axis \\ \end{tabular} & 0.76 & 75.5 \\ \hline \end{tabular}
\end{table} 
Table 1: Elements causing \(\varphi_{2}\) axis load with their mass and lever arms. Figure 10: View of the elements causing \(\varphi_{2}\) axis load before assembly. The correct definition of this area is a critical element of the system's operation. It is possible to read the external force vector acting on the device during movement.