# Vision-Based Path Guidance to Achieve Dies-Free Roller Hemming Process
## 3 Verification and Results
### Hemming Experiment and Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & \multicolumn{10}{c}{**Unit: mm**} \\ \hline  & & \multicolumn{3}{c}{**Patt**} & \multicolumn{3}{c}{**Part**} & \multicolumn{3}{c}{**Part**} & \multicolumn{3}{c}{**XYZ Offset**} & \multicolumn{3}{c}{**Distance**} \\  & & \multicolumn{3}{c}{**Robot Pose**} & & \multicolumn{3}{c}{**A**} & \multicolumn{3}{c}{**B**} & \multicolumn{3}{c}{**C**} & \multicolumn{3}{c}{**among 3 Parts**} & \multicolumn{3}{c}{**Error \(\epsilon\)**} \\ \hline  & X & 1517.209 & W & \(-\)179.888 & X & 0.192 & 0.192 & 0.197 & dX & 0.005 & \\ P5 & Y & \(-\)568.234 & P & 0.473 & Y & \(-\)2.170 & \(-\)2.619 & \(-\)4.676 & dY & 2.506 & 4.461 \\  & Z & 641.432 & R & \(-\)76.687 & Z & \(-\)3.375 & \(-\)3.734 & \(-\)7.066 & dZ & 3.691 & \\ \hline  & X & 1659.402 & W & \(-\)179.888 & X & 0.191 & 0.191 & 0.197 & dX & 0.006 & \\ P6 & Y & \(-\)565.426 & P & 0.473 & Y & \(-\)1.530 & \(-\)1.781 & \(-\)3.754 & dY & 2.224 & 4.278 \\  & Z & 627.715 & R & \(-\)73.193 & Z & \(-\)2.539 & \(-\)2.678 & \(-\)6.193 & dZ & 3.654 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(Cont.\)  
Figure 17: Screenshot of the software to visualize the real-time compensation path for hemming. After the flange was hemmed, measurements of the roll-in/roll-out displacement error and the surface flatness, which are the two key measures of concern in the automobile industry, were conducted. The definition of the roll-in/roll-out displacement error is best illustrated in Figure 18b. As shown in Figure 18b, this displacement error is positive when the hemmed sheet's contour edge is left off or out of the original vertical flange. On the other hand, the roll-in error gives a negative value as the hemmed sheet's contour edge is in the right-hand side or inside the region where the original vertical flange was being hemmed to. In engineering practice, to ensure the hemmed sheet metal plate will provide suitable force onto the inner sheet metal, this roll-in/roll-out displacement error actually is the key design factor when sheet metal parts are connected through the hemming process. The roll-in/roll-out displacement error of the 9 mm and 10 mm flange height steel sheets after the hemming process are plotted in Figure 19, where the measuring location is along the hemmed part's out-of-the-plane direction in Figure 18. With the proposed vision-based path guidance and the calibration method, one can observe that the roll-in/roll-out displacement errors are well within the \(\pm\)0.25 mm specification (red lines) set by industry acceptance standards. The error becomes a little bigger around 170-180 mm, probably caused by the unbalanced force between the roller and the metal sheet when the robot reached the end of the 180 mm wide metal sheet. For the surface flatness measurement, as show in Figure 20, a non-contact laser displacement sensor, the Micro-Epsilon scan CONTROL 2900-10/BL, with out-of-plane accuracy of 0.02 mm was used to scan along the \(x\)-axis of the sheet at intervals of 0.05 mm. Results of surface flatness of the hemmed edge surface from the 9 mm flange height flat sheet metal through the forward hemming is shown in Figure 21. It is observed that the surface flatness of the hemmed sheet is well below the industry acceptance standard of \(\pm\)0.25 mm. The maxima surface flatness of the sheet, being not very flat, is in the starting  
Figure 19: Measured roll-in/roll-out displacement error of after being hemmed. Figure 18: Schematic drawings showing (**a**) the sheet metal hemming experiment and (**b**) the definition of the contour edge roll-in/roll-out displacement error. location when the hemming process takes place. Such non-flatness can be eliminated when the robot is undertaking backward hemming after forward hemming is completed. In general, the surface flatness of the hemmed sheets can be below \(\pm\)0.05 mm by using the proposed method and system.