# Influence of the Approach Direction on the Repeatability of an Industrial Robot
## 5 Experimental Results  
To confirm the hypothesis that the endpoint repeatability depends, among other things, on the direction of approach to this point, it was necessary to realize the selected measurements in three different ways. For each of these measurements, a set of starting points was created, then three different measurements were executed under the same conditions, with the difference that in the first measurement the points were selected in order from the lowest to the highest value of the \(y\)-axis (\(y_{\text{MIN}}\)\(\rightarrow\)\(y_{\text{MAX}}\)), the second measurement was in the opposite direction (\(y_{\text{MAX}}\)\(\rightarrow\)\(y_{\text{MIN}}\)) and in the third one, the points were chosen in random order. The joint variables (\(\text{j}_{1}\)--\(\text{j}_{6}\) (\({}^{\circ}\))) were always read and then the values for the same points were compared when measuring in a different overall order. From the graphs (Figure 7) it is evident that the deviation depends only on the position of the starting point relative to the endpoint. Whether these starting points for the approach are selected in order from one side or the other one, or completely randomly, is not important. This result, among other things, excludes accidental errors or other influences that would cause randomness in these results. The waveforms of individual measurements almost completely overlap with only a minimal difference between the first \"yellow\" measurement (\(y_{\text{MIN}}\)\(\rightarrow\)\(y_{\text{MAX}}\)), in which the points were executed from the lowest \(y\)-axis value to highest. Red (\(y_{\text{MAX}}\)\(\rightarrow\)\(y_{\text{MIN}}\)), was executed in the opposite order and blue using a completely random order of points. All three waveforms have been sorted from \(Y_{\text{MIN}}\) to \(Y_{\text{MAX}}\), due to the possibility of comparing the same points in these measurements. According to the mathematical model, the position and deviations of the tool center point can be calculated based on the forward kinematics task, but this value varies in the spectrum of absolute inaccuracy. To determine the repeatability and the real deviations from the selected target, it is necessary to measure the precision at the endpoint (TCP). For this purpose, the 3D DIC methodology will be applied in the second phase, to verify the results. Figure 7: Deviations of joints (\({}^{\circ}\)) in the ordered and random selection of default positions. Individual measurements are also shown in the form of box-plot graphs, its principle is described in Figure 8. Symbols represent values outside the basic range (outliers). If the value is greater than three times the quartile, it is displayed with the symbol \"o\", the symbol \"+\" is used to display the value in the range 1.5-3 [35]. The graphs below (Figures 9 and 10) show the influence of the approach direction on the individual joint variables of the robot. As already mentioned in the article, these data come from the drive resolvers of the individual axis of the robot, i.e., they do not include errors that occur \"higher\" on the structure. Figure 8: (**A**): Quantile of measured values [36]. (**B**): Symbols displaying values outside the basic range. Figure 9: Error (°) distribution on individual robot joints during Measurement 14. The figures (Figures 9 and 10) show data from robot drive resolvers--the results of Measurements 14 and 16 according to tables (Tables 6 and 7). All the realized measurements were evaluated in this way. However, to better understand the facts found, and especially to determine the real precision of the manipulator, it is necessary to convert these data to repeatability values on the endpoint of the robot, i.e., the TCP point (see Figure 11). This recalculation is realized by the generally known methodology of the forward kinematics task, the Denavit-Hartenberg parameters used for this recalculation are described in Table 9 below. Figure 11 below displays the overall deviations of the TCP, calculated from given D-H parameters.