# Industrial Robot Positioning Performance Measured on Inclined and Parallel Planes by Double Ballbar
## 2 Motivation  
As indicated in the introduction, several measurements with the Renishaw Ballbar QC20-W involving industrial robots were carried out in the past at the Department of Automation and Production Systems, and the results have been published [25; 26; 27; 28]. In most cases, these were basic measurements in the XY plane, parallel to the base plane of the WCS (World Coordinate System) and, at the same time, parallel to the robot base. The measurements were done on Fanuc robots, where the WCS is represented by a fixed coordinate system defined by the manufacturer. The same orientation of the measuring plane in the robot's workspace has been chosen by other authors in their papers too [19; 21; 22]. The said basic type of measurement requires completing two circular paths in the XY plane in a clockwise direction (CW) and two circular paths in the opposite direction (CCW) [31; 32]. Figure 1 shows the course of the motion of the individual robot joints (J1 through J6), during the TCP movement in a circular path in the clockwise direction. The graph shows data that was created in the Creo Parametric 5.0.4.0 program using movement simulation of the model of the Fanuc LR Mate 200 iC robot, with the simulation conditions given in Table 1.  
The graph in Figure 1 shows that when the measuring is done in the XY plane, the J4 joint is static for the entire duration of the TCP moving along the circle, therefore, it can be said that the results do not take into account the possible negative effect of the J4 joint motion or that the given results correspond to only one specific position from the range of the J4 joint motion. Regardless of the above statement, the measurement in the XY plane is informative and can be used to evaluate the robot's technical condition. For example, in one of our papers [25], a measurement in the XY plane was used to evaluate the effect of calibration on the accuracy of the resulting movement of the robot's TCP. In the case of CNC machine tools, to evaluate the effect of movement of all three linear axes (X, Y, and Z), the so-called volumetric analysis, consisting of measurements in three mutually perpendicular planes XY, ZX, and ZY, is used. During the measurement in the XY plane (see Figure 2a) two standard clockwise and two counterclockwise circles are made. In the ZX and ZY planes (see Figure 2b,c) two semicircular paths in the range of 220\({}^{\circ}\) are measured, again one in the clockwise and the other in the counterclockwise direction [33; 34]. To verify the possibilities of the volumetric analysis application on industrial robots, a series of measurements were performed in the past on two industrial robots Fanuc LR Mate 200 iD and LR Mate 200 iD/7L. The circular path and circular arcs with a radius of 100 mm, necessary for measurement purposes, were created through standard programming commands for Fanuc robots. Further information on the measurement conditions is given in Table 2. \begin{table}
\begin{tabular}{c c} \hline \hline
**Type of Industrial Robot** & **Fanuc LR Mate 200 iC** \\ \hline The radius of circular paths & 100 mm \\ Centre of circle relative to WCS (X; Y; Z; W; P; R) & 300; 500; \(-\)253.5; 0; 0; 0 \\ Coordinates of the TCP (X; Y; Z) & 0; 0; 74.65 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Conditions for creating the circle in the XY plane. Figure 1: The course of the motion of the individual robot joints during the TCP movement in a circular path in the XY plane. Figure 2: Circular paths in individual planes for volumetric analysis. (a) plane XY; (b) plane ZX; (c) plane ZY. The measurements were evaluated in the Ballbar 20 software, with Figures 3 and 4 showing polar graphs of one of thirty repeated measurements for each plane and for both Fanuc robots. In addition to a more detailed analysis of the measurement results, two observations are important for the purposes of this paper. The first is the \"solid line\", which is apparent on the polar graphs for the ZX and ZY planes when measured on the LR Mate 200 iD/7L robot (Figure 4).