# Suitability of UR5 Robot for Robotic 3D Printing
## 4 Methodology and Conditions for Measuring the UR5 Collaborative Robot
### Assessing the Drift Test of Unidirectional Pose Accuracy (dAP)  
In the test (dAP), 49 measurements were performed at measurement point P1, with a maximum load of 100% and a maximum motion speed of 100%. The overview data (dAP) of the results of the calculated values are shown in Table 1. The drift measurements were carried out cold (immediately after the power supplies were put into operation) and run for several hours until the robot was warmed up. The robot was programmed to move its mechanical interface (interface) to P1 starting from P2. When returning from P1 to P2, all robot joints moved.  
When comparing the drift of unidirectional pose accuracy, we used the value specified by the manufacturer, namely, the value of unidirectional pose repeatability \(\pm\)0.1 mm. Since none of the measured values exceeded the prescribed value, we concluded that the robot passed the test.  
The calculation of the drift of the unidirectional accuracy dAP is expressed as follows:  
\[\mathrm{dAP}=\left|\mathrm{AP}_{t=0}-\mathrm{AP}_{t=T}\right| \tag{1}\]  
whereas the value of AP (unidirectional pose accuracy) is derived from Equations (2)-(4),  
\[\mathrm{AP}=\sqrt{\left(\overline{x}-x_{c}\right)^{2}+\left(\overline{y}-y_{ c}\right)^{2}+\left(\overline{z}-z_{c}\right)^{2}} \tag{2}\]  
\[\mathrm{AP}_{x}=\left(\overline{x}-x_{c}\right);\ \mathrm{AP}_{y}=\left( \overline{y}-y_{c}\right);\ \mathrm{AP}_{z}=\left(\overline{z}-z_{c}\right) \tag{3}\]  
where (\(x_{c}\), \(y_{c}\), \(z_{c}\)) are the programmed values, and (\(x_{j}\), \(y_{j}\), \(z_{j}\)) are the measured values. The barycenter coordinates of the points reached in \(n\) repetitions of the same position are computed using the following equations:  
\[\overline{x}=-\frac{1}{n}\sum_{j=1}^{n}x_{j}\quad\overline{y}=\frac{1}{n}\sum _{j=1}^{n}y_{j}\quad\overline{z}=\frac{1}{n}\sum_{j=1}^{n}z_{j} \tag{4}\]  
The resulting drift of the unidirectional accuracy (\(\mathrm{dAP}_{\mathrm{a}}\), \(\mathrm{dAP}_{\mathrm{b}}\), \(\mathrm{dAP}_{\mathrm{c}}\)) of the orientation is derived as follows:  
\[\mathrm{dAP}_{a}=\left|\mathrm{AP}_{a_{t}=0}-\mathrm{AP}_{a_{t}=T}\right|;\ \mathrm{dAP}_{b}=\left|\mathrm{AP}_{b_{t}=0}-\mathrm{AP}_{b_{t}=T}\right|;\ \mathrm{dAP}_{c}=\left|\mathrm{AP}_{c_{t}=0}-\mathrm{AP}_{c_{t}=T}\right| \tag{5}\]  
with \(\mathrm{AP}_{\mathrm{a}}\), \(\mathrm{AP}_{\mathrm{b}}\), and \(\mathrm{AP}_{\mathrm{c}}\) derived from Equations (6) and (7). The procedure for calculating the unidirectional accuracy of the orientation is based on  
\[\mathrm{AP}_{a}=\left(\overline{a}-a_{c}\right);\ \mathrm{AP}_{b}=\left( \overline{b}-b_{c}\right);\ \mathrm{AP}_{c}=\left(\overline{c}-c_{c}\right) \tag{6}\]  
Figure 5: Arm of the UR5 robot with the measuring cube mounted.  
The graph presented in Figure 6 displays the plot of the calculated drift values of the unidirectional pose accuracy (dAP) in three mutually perpendicular directions during a measurement lasting 8 h. The calculated average value is dAP = 0.072447154 < 0.1 mm.  
The following graph, presented in Figure 7, displays the plot of the computed drift values of the unidirectional pose accuracy (dAP\({}_{a}\), dAP\({}_{b}\), and dAP\({}_{c}\)) in two mutually perpendicular directions. The graphical representation shows that the average drift values of the unidirectional orientation accuracy are dAP\({}_{a}\) = 0.0684450883 < 0.1 mm, dAP\({}_{b}\) = 0.0367866413 < 0.1 mm, and dAP\({}_{c}\) = 0.0752525250 < 0.1 mm.  
In the case of convergence of the partial parameters (dAP\({}_{s}\)) to the designed AP values over the entire range of the 8 h measurement time, the parameter \"complies\" with the manufacturer's specified data.