# Influence of the Approach Direction on the Repeatability of an Industrial Robot
## 6 Verification of the Results and Determination of Real TCP Deviations Using DIC
\begin{table}
\begin{tabular}{c c} \hline \hline
**Measurement Area** & **Adjustable: From mm\({}^{2}\) to m\({}^{2}\)** \\ \hline Measuring range & Displacement: approx. \(10^{-5}\) of the field of view, which corresponds to 1 \(\upmu\)m at a field \\  & size of 100 mm, strains: from 0.01\%–several 100\% \\ Resolution & max. 1280 \(\times\) 800 px up to the scan frequency of 3140 FPS \\ Measurement results & The spatial contour of the object surface, 3D displacements, strains at each point, spectral analysis \\ Control and monitoring electronics & portable laptop with Windows 7 operating system, 16-bit analogue-to-digital converter (8 channels with a voltage range of \(\pm\)0.05 V to \(\pm\)10 V) \\ lighting & halogen reflector with white light \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Technical parameters of the Q-450 Dantec Dynamics system. Figure 15: Measurement of IRB1200 by DIC Q-450 system. Figure 16: Illustrative example of the increase of the image resolution caused by the facet overlap: (**A**): defined area of interest, (**B**): measuring points when the facets are in touch, (**C**): measuring points when the facets are overlapped. Figure 17: The scheme of the transformation of the analyzed point world coordinates into the sensor coordinates. To obtain information about the transformation coordinates of the points of the analyzed object, Dantec Dynamics correlation devices use an algorithm based on a pseudo-affine transformation [38]. If the transformation parameters of possible displacement, elongation, shear, and distortion of the facet \(a_{0}\)-\(a_{7}\) (Figure 18) are considered, according to the above-mentioned algorithm the transformation coordinates (u, v) can be calculated as follows:  
\[ \begin{array}{l}u(a_{0},a_{1},a_{2},a_{3},\overline{x},\overline{y})=a_{0}+a_ {1}\overline{x}+a_{2}\overline{y}+a_{3}\overline{x}\overline{y}\\ u(a_{4},a_{5},a_{6},a_{7},\overline{x},\overline{y})=a_{4}+a_{5}\overline{x}+a_ {6}\overline{y}+a_{7}\overline{x}\overline{y}\end{array}  \tag{1}\]  
The measurement procedure was the same as in the case of robot joint variables measurement. The flowchart (Figure 4) was only extended (Figure 19) as follows (three images are always taken):  
Figure 19: Flowchart of the experiment control system (DIC). To determine the effect of robot drift, Measurement 4 (Table 1, Figure 20) was performed. Drift can seriously affect the repeatability and accuracy if the robot structure temperature changes significantly. The drift could be prevented by keeping the structure at the optimal working temperature (by cooling in with fans in foundry applications, for example). Measurement 4 results however, proved, that for conditions under which all the measurements took place, the influence of drift is not significant. The pre-warm-up routine was used before every measurement to get the system to its optimal operating temperature. According to the \"3D Map (Figure 21) it is evident, that at a given position of the point relative to the robot, the repeatability can be increased simply by changing the direction of approach to the target Figure 21 shows Measurements 14 and 16 (radius 250/300 mm, 40 different default positions, different carried weight) displaying its total errors. The points are sorted from YMIN to YMAX i.e., from the bottom of the semi-sphere to its top. From the figures, it is apparent that under the defined conditions, the most convenient direction of approach is from the VII octant for Measurement 14 and the top (\(z\)-axis) in case of Measurement 16. For the selected measurements, the real repeatability values (mm) measured by DIC are displayed in Figures 22 and 23. From the Measurement 14 results (Figure 22), it is evident that the carried weight influences the repeatability predominantly in the middle sections (mid-range of point's y value) of error graphs. In the case of Measurement 16 (Figure 23), the difference in repeatability values within the measured hemisphere is not significant. Figure 20: Manipulator repeatability (mm), Measurement 4.