# Industrial Robot Positioning Performance Measured on Inclined and Parallel Planes by Double Ballbar
## 5 Measurement with Renishaw Ballbar QC20-W

Table 4: Measurement conditions. Figure 10: Polar graphs from measuring a circle on the inclined plane. **(a)** NOFLIP configuration; **(b)** FLIP configuration. these errors can be attributed mainly to the incorrect conversion of Cartesian coordinates, related to the direct kinematic task, and the issue of calibration. Specifically, this is the first level calibration, related to the relationship between the actual position of the robot arm and the information from the encoders in its individual joints [39]. For a more detailed analysis of the measurements, based on the robot's simulation model, a graph was created in Figure 11. This graph shows the range of motion of the robot's individual joints during measurements with both configurations of the robot arm. The graphical representation shows that the movements of the joints J1, J2, and J3 are identical in both configurations. On the contrary, the changes occur only in the orientation of the robot's subsystem, i.e., that of the joints J4, J5, and J6. Based on this analysis, it can be concluded that the change in the shape of the polar graphs (Figure 10) is caused by one of the joints of the robot's orientation subsystem, or a combination thereof. A more accurate identification of the specific robot joint or joints that adversely affect the measurement results can be addressed in several ways. This involves, for example, limiting the motion of one of the robot's examined joints, or modifying the motion of the joint so that its possible adverse effect is apparent. The graph in Figure 11 shows that the motion of the J6 joint is shifted by 180\({}^{\circ}\) relative to each other in both configurations. At the same time, the coordinates of the TCP orientation are constant during the entire circular motion and have the following values (W = 180\({}^{\circ}\); P = 0\({}^{\circ}\); R = 0\({}^{\circ}\)). Because the TCP is in the axis of rotation of the J6 joint, the coordinate \"R\" (rotation around the Z-axis) can influence the way the joint J6 moves. This theory was first verified in the robot's simulation model. For an arm configuration with J5 > 0\({}^{\circ}\) (FLIP), a TCP position was defined with the coordinate R adjusted to 180\({}^{\circ}\). The graph in Figure 12 shows that by applying the said change, the same motion of the J6 joint was achieved as in the NOFLIP configuration. At the same time, there was no change in the J4 and J5 joints. Figure 11: Comparison of the movement of robot joints for both used robot arm configurations. Figure 12: Impact of TCP coordinate modification on the movement of robot joints. Subsequently, practical measurements were done, with a change applied to individual points of the control program with the adjustment of the coordinate R = 180\({}^{\circ}\). The conditions of this measurement were identical to the conditions from Table 4, with the number of repeated measurements being ten. The resulting polar graph is shown in Figure 13c. In comparison to previous measurements (Figure 13a,b), it is apparent that the change in the motion of the J6 joint does not affect the shape of the polar graph. This fact is also confirmed by the average value of circularity given in Table 6, while the difference of 20.4 \(\upmu\)m can be considered negligible. Based on the presented results, it can be argued that the change in the shape of the polar graph is caused by the joint J4 or J5, or a combination thereof.