## 3 Experimental Results and Discussion
### Results and Discussion  
To analyze the measurement accuracy of the experimental vision system, the screw-tool engagement based on a robot vision was performed 20 times in the same manner for each screw (#1, #2 and #3) in a random position. The desired position \((x_{real},y_{real},z_{real})\) and the angular offset \(\theta_{real}\) of each screw were calibrated by the manually teaching of a robot and used to calculate the corresponding error between the calculated and desired values, i.e., \((x_{cal},y_{cal},z_{cal})\) and \(\theta cal\). The largest errors are listed in Table 4, where \(\Delta x=\mid x_{real}-x_{cal}\mid\), \(\Delta y=\mid y_{real}-y_{cal}\mid\), \(\Delta z=\mid z_{real}-z_{cal}\mid\), \(\Delta=\sqrt{\Delta x^{2}+\Delta y^{2}}\), and \(\Delta\theta=\theta_{real}-\theta_{cal}\). Error \(\Delta\) indicates a displacement offset between the calculated and desired positions of the screw center on the plane it was located on, which directly demonstrated whether the engagement succeed or not. According to the obtained results, the largest value of the error \(\Delta\) was 0.856 mm. It should be noted that there must exist the measurement error due to affecting factors such as uncertainties during the procedures of camera calibration and image processing. However, there was a gap of 0.88 mm between the bottom of the unfastening tool and the screw head, which could guarantee the next engagement and unfastening actions. In addition, the results in Table 4 show that errors in the normal direction were generally larger than in the other directions, which was mainly because the normal position acquisition based on robot vision did not completely rely on image processing, and also the object distance estimation of the monocular camera. Variations in the torque of the three screws with the time under different settings are shown in Figure 23. The screws were disassembled at different rotating velocity values of \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Screws** & \(\Delta x\) **(mm)** & \(\Delta y\) **(mm)** & \(\Delta z\) **(mm)** & \(\Delta\) **(mm)** & \(\Delta\theta\) **(deg)** \\ \hline \#1 & 0.483 & 0.376 & 2.136 & 0.612 & 0.41 \\ \#2 & 0.265 & 0.814 & 2.469 & 0.856 & 0.73 \\ \#3 & 0.327 & 0.659 & 0.196 & 0.735 & 0.65 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Errors between the calculated and desired screw poses. Figure 22: Detailed flowchart of the unfastening strategy used in the experiment. 90 rpm, 120 rpm, 150 rpm, and 180 rpm. After engaging between the tool and the screw, it took 1.778 s, 1.418 s, 1.067 s, and 1.0 s to unfastening #1 screw under the cooperation motion of the manipulator and tool. The curve of #1 screw in Figure 23a shows that the torque firstly reached 4.9 N\(\cdot\)m after the tool had started working and then rapidly decreased to approximately 2.4 mm/s when \(w\) = 90 rpm. The average unfastening torque increased from 2.44 mm/s to 3.27 mm/s when the rotating speed of the tool increased from 90 rpm to 180 rpm. For the curves of #2 and #3 screws, variations in the torque showed a similar trend. Since the wear of holes and screws differed, curves obtained under three cases were not identical. The thread contact between the screw and the hole was intensified due to higher motion speeds, so a larger torque was generated. Also, a greater vibration was generated under the higher speeds, which could cause higher instability of the torque. The standard deviation was used to evaluate torque fluctuations. As shown Figure 24, the standard deviation of the torque of the three screws increased with the rotating speed. For instance, the standard deviation of #1, #2, and #3 screws increase by 20.49%, 30.37%, and 25.85%, respectively, when the speed increase from 90 rpm to 180 rpm. The results indicated that the torque fluctuation had a negative effect on the thread quality of the workpiece, which is important for some reusable and long-serving workpieces.