# Industrial Robot Positioning Performance Measured on Inclined and Parallel Planes by Double Ballbar
## 5 Measurement with Renishaw Ballbar QC20-W
### Measurement in a Plane Parallel to the Robot's Base  
The series of measurements was further supplemented by the measurement of a circular path when the XY plane formed an angle of 0\({}^{\circ}\) with the benchtop. The second of the already mentioned jigs was used for this measurement (Figure 7c), which ensured that the central position of the circle was identical to its central position in the previous measurements. Compared to measurements on an inclined plane, the ranges of motions of the individual robot joints are different, with the J4 joint not participating in the movement and its rotation has a constant value throughout the measurement. The absolute values of the range of motion of the individual robot joints measured on an inclined plane (at an angle of \(-45^{\circ}\)) and a plane parallel to the base of the robot (angle 0\({}^{\circ}\)) are shown in the graph in Figure 14. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Configuration** & **Configuration** & **Configuration** \\  & **NOFLIP** & **FLIP** & **FLIP\({}^{\prime}\)** \\ \hline Circularity [\(\upmu\)m] & 652.2 & 409.8 & 389.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Average circularity value for measuring a circle on the inclined plane. Figure 14: Absolute angular movement of robot joints during the movement along a circular path in both measuring planes. Figure 13: Polar graphs from measuring a circle on the inclined plane. (**a**) NOFLIP configuration; (**b**) FLIP configuration; (**c**) FLIP\({}^{\prime}\) configuration (coordinate R = 180\({}^{\circ}\)). There are also two possible configurations of the robot arm for the selected position and orientation of the circle. For the configuration with the joint position J5 \(<\) 0\({}^{\circ}\) (NOFLIP), the J4 joint has a constant value of 0\({}^{\circ}\) throughout the path traveled. The circular path can also be completed with the second configuration, i.e., J5 \(>\) 0\({}^{\circ}\) (FLIP), but in this case, the J4 joint acquires the limit values of its range of rotation, which are +180\({}^{\circ}\) or -180\({}^{\circ}\). Such position of the robot arm, with limit values of one of the joints, is unsuitable due to the restriction on further movements, but it can meet the purpose of the measurement. At the same time, to ensure that the range of motion of the J6 joint was the same for all three mentioned positions of the robot arm in the measurement process, the \"W\" coordinate of individual points forming the circle was again adjusted to 180\({}^{\circ}\) in the FLIP configuration. The ranges of motions of the J4, J5, and J6 joints, when moving along the circular path, are shown in the graph in Figure 15. Again, as in the previous cases, positional analysis in the Creo Parametric system 5.0.4.0 was used to chart this graph. For the sake of simplicity, the graph does not include the range of motions of the J1, J2, and J3 joints, which are identical for all positions of the robot arm used. Measurements with the Renishaw Ballbar QC20-W were conducted under the same conditions as in Table 4, except for the orientation of the center of the circular path, which is zero (W = 0\({}^{\circ}\); P = 0\({}^{\circ}\); R = 0\({}^{\circ}\)) in the present case. The individual polar graphs are shown in Figure 16 and the average circularity values from ten repeated measurements for each robot arm position used are shown in Table 7.  
When comparing the resulting polar graphs, the first thing to be observed is the similarity between the measurements with the FLIP configuration of the arm. The similarity is also indicated by the value of circularity shown in Table 7, the resulting difference is negligible. During both measurements in the FLIP configuration, the motions of all joints were identical except for the J4 joint, which did not take part in the movement along the circular path but acquired a different limit value in both cases.