# Suitability of UR5 Robot for Robotic 3D Printing
## 4 Methodology and Conditions for Measuring the UR5 Collaborative Robot
### Assessing the Static Compliance (SC) Test
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**SC** & & **X (+)** & & & **X (-)** & \\ \hline Load & 5 N & 25 N & 50 N & 5 N & 25 N & 50 N \\ x\({}_{1}\) & 0.028 & 0.102 & 0.186 & 0.025 & 0.091 & 0.211 \\ x\({}_{2}\) & 0.031 & 0.092 & 0.189 & 0.009 & 0.121 & 0.208 \\ \({}_{3}\) & 0.039 & 0.093 & 0.198 & 0.018 & 0.115 & 0.198 \\ Average value [mm] & 0.032667 & 0.095667 & 0.191000 & 0.017333 & 0.109000 & 0.205667 \\  & & Y (+) & & Y (-) & \\ Load & 5 N & 25 N & 50 N & 5 N & 25 N & 50 N \\ y\({}_{1}\) & 0.062 & 0.527 & 1.115 & 0.070 & 0.517 & 1.145 \\ y\({}_{2}\) & 0.059 & 0.507 & 1.189 & 0.058 & 0.501 & 1.103 \\ y\({}_{3}\) & 0.077 & 0.523 & 1.126 & 0.066 & 0.495 & 1.056 \\ Average value [mm] & 0.066000 & 0.519000 & 1.143333 & 0.064667 & 0.504333 & 1.101333 \\  & & Z (+) & & & Z (-) & \\ Load & 5 N & 25 N & 50 N & 5 N & 25 N & 50 N \\ z\({}_{1}\) & 0.036 & 0.266 & 0.631 & 0.035 & 0.178 & 0.318 \\ z\({}_{2}\) & 0.056 & 0.269 & 0.597 & 0.031 & 0.155 & 0.324 \\ \({}_{3}\) & 0.029 & 0.204 & 0.585 & 0.039 & 0.143 & 0.320 \\ Average value [mm] & 0.040333 & 0.246333 & 0.604333 & 0.035000 & 0.158667 & 0.320667 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Measured values of the UR5 robot static compliance. Figure 11: Schematic of the static compliance measurement of the UR5 robot and the measurement means employed; (**a**) simplified schematic representation, (**b**) display of components in 3D view. where \(F_{j}\) is the loading force (load), and \((x_{j},y_{j},z_{j})\) are the actual (measured) deflection values:  
\[\overline{x}=-\frac{1}{n}\sum_{j=1}^{n}x_{j};\ \ \ \overline{y}=-\frac{1}{n}\sum_{j=1}^{n}y_{j};\ \ \ \overline{z}=-\frac{1}{n}\sum_{j=1}^{n}z_{j} \tag{16}\]  
with \(\overline{x},\ \overline{y},\ \overline{z}\) being the arithmetic averages of the measured deviation values. The overview data of static ductility from the results of the calculated values are indicated in Table 5 for the directions of the (\(\pm\)) X, Y and Z-axes. Static compliance is specified in millimeters of displacement in each direction and in terms of load per 1 N of load relative to the base coordinate system. The arithmetic mean was calculated from the measured values for each direction and sense of loading force. The calculated average values of the static compliance of the UR5 robot in the (\(\pm\)X) axis were SC\({}_{\rm x}\) = 0.004353333 mm/N; in the (\(\pm\)Y) axis, SC\({}_{\rm x}\) = 0.019866667 mm/N; and in the (\(\pm\)Z) axis, SC\({}_{\rm x}\) = 0.00829444 mm/N. Since the manufacturer did not specify a value for this parameter in its technical documentation, the test result was only \"declared\". An example of a static compliance measurement is displayed in Figure 12. The figure shows the measurement at point P1 using a measuring ball and an array of three sensors placed around the perimeter of the measuring nest. Figure 12: Static compliance measurement at P1 point. \begin{table}
\begin{tabular}{c c c c c c} \hline  & & **X (+)** & & **X (c)** & \\ \hline Load & 5 N & 25 N & 50 N & 5 N & 25 N & 50 N \\ Static Compliance & 0.00653 & 0.00382 & 0.00382 & 0.00346 & 0.00436 & 0.00411 \\ (mm/N) & & Y (+) & & & Y (c) & \\ Load & 5 N & 25 N & 50 N & 5 N & 25 N & 50 N \\ Static Compliance & 0.01320 & 0.02076 & 0.02286 & 0.02017 & 0.02017 & 0.02202 \\ (mm/N) & & Z (+) & & & Z (c) & \\ Load & 5 N & 25 N & 50 N & 5 N & 25 N & 50 N \\ Static Compliance & 0.00806 & 0.00985 & 0.01208 & 0.00700 & 0.00634 & 0.00641 \\ (mm/N) & & & & & & \\ \hline \end{tabular}
\end{table} 
Table 5: Calculated values of static compliance of the UR5 robot.