## 3 Standardization ISO 9283--Path Accuracy  
Conditions for conducting measurements must comply with the recommendations of the manufacturer, especially when it comes to installation. The robot should be functioning and installed correctly from the manufacturer's point of view, and all its balancing should be appropriate. If a start-up phase is indicated, it should be performed. The standard sets the ambient temperature at 20 \(\pm\) 2 \({}^{\circ}\)C or ranging between 5 and 40 \({}^{\circ}\)C. The measurements \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Laser Transmitter** & **GEPARD 5 bt** & **Laser Receiver** & **GEPARD 5 bt** \\ \hline Laser power & \textless{}1 mW & Measuring range & \(15\times 15\) mm \\ Laser class & 2 & Measurement resolution & 0.5 mm \\ Wavelength & 650 nm & Linearity & 0.04\% \\ Beam cross-section & circle & Repeatability & \(\pm\)0.25 \(\upmu\)m \\ Power supply & Li-on 7.2 V & Power supply & Li-on 7.2 V \\ Dimensions & 142 \(\times\) 50 \(\times\) 50 mm & Dimensions & 142 \(\times\) 50 \(\times\) 50 mm \\ Weight & 730 g & Temperature range & 10–45 \({}^{\circ}\)C \\ Beam adjustment & Yes & Measuring distance & 0–15 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Table of parameters GEPARD 5 bt system. Figure 3: Representation of the measure taken via the ISO line. were performed at the ambient temperature of 20 \({}^{\circ}\)C on the collaborative robot FANUC CRX-10 iA (Yamanashi, Japan) with a suitable control cabinet and a pendant. Verification was performed using a mechanical flange interface connected to the measuring device, with a maximum load of 10 kg. The measured path was set on a measuring plane as prescribed by the standard [5; 24]. Definitions of the path accuracy and repeatability do not depend on the shape of the programmed path. Two examples of the programmed paths' different shapes are shown in Figures 4 and 5 [25]. Path accuracy describes the robot's ability to move through its interface along the programmed path n-times in one direction and n-times in the opposite direction. Path accuracy is determined by two factors:  
* A difference between the programmed path and the barycentric line of the set of paths taken, Figure 4;
* A difference between the programmed angular orientation and the mean value of the angular orientation achieved (accuracy of the path orientation). Thus, path accuracy is the utmost path deviation obtained during positioning and orientation. Accuracy of the path positioning, \(AT\), is defined as the utmost distance between  
Figure 4: Path accuracy for the linear path. Figure 5: Path accuracy for the circular path. the programmed path and the barycenters \(G_{in}\) in measurements of each of the number of measuring points (\(m\)) along the path [26]. If the programmed path is defined as the axis Z, then the path-positioning accuracy will be calculated from the following equation:  
\[AT=\underset{i=1}{m}\sqrt{(x_{ci}-\overline{x_{i}})^{2}+(y_{ci}-\overline{y_{i}} )^{2}} \tag{3}\]  
\[AT_{x}=\underset{i=1}{m}\ |(x_{ci}-\overline{x_{i}})| \tag{4}\]  
\[AT_{y}=\underset{i=1}{m}\ |(y_{ci}-\overline{y_{i}})| \tag{5}\]  
whereas  
\[\overline{x_{i}}=\frac{1}{n}\sum_{j=1}^{n}x_{ij} \tag{6}\]  
\[\overline{y_{i}}=\frac{1}{n}\sum_{j=1}^{n}y_{ij} \tag{7}\]  
where  
\(x_{ci},\ y_{ci}\) --point coordinates on the programmed path corresponding to the measuring point \(z_{i}\). \(x_{ij},\ y_{ij}\)--point coordinates of the achieved path corresponding to the measuring point \(z_{i}\) for \(j\)th repetition. Accuracies of the _ATa_, _ATb_, and _ATc_ path orientation are defined as the utmost deviation from the programmed angles along the path. However, this experimental method does not allow for their exact determination [27]. While the path-accuracy definition defines path accuracy as a distance-dependent value, measuring the achieved path may be performed either as a function of distance or of time. Where significant speed fluctuations along the path are present, repeated measurements must be performed as a function of time.