## 2 Proposed Screw Unfastening Strategy
### Screw Unfistening Method Based on Cooperated Motion  
As shown in Figure 20, the unfastening motion is realized through the cooperation of the rotational motion of the unfastening tool and the robotic motion along the axial direction of a screw. For the cooperated motion, the angular velocity \(w\) of the unfastening tool and the linear velocity \(v_{r}\) of the robotic end effector should be set properly. If the value of \(v_{r}\) is much higher than the normal speed \(v_{s}\) of a screw, the screw will break away from the tool before the screw leaves the hole. In contrast, if the value of \(v_{r}\) is too small, there can be two negative effects. First, the spinning of the hexagonal screw may seriously damage the hole. Second, the normal force \(F\) can be generated between the tool and the workpiece, which can severely damage the thread surface quality of a workpiece. In this work, values  
Figure 19: Relative relation between a screw and the tool.  
of \(w\) and \(v_{r}\) are set based on Equation (8), which can help to improve the motion stability. Using Equation (8), the cooperated motion of a robot and the unfastening tool is planned based on the screw pitch, which is determined according to the national standard gb/t 5783-2000 and a specific type of screw. Therefore, in the proposed strategy, the screw type needs to be known in advance. Additionally, the proposed system is applicable only to screws with the same size \((M10)\) since the end size of the unfastening tool is fixed.  
\[v_{r}=w/360\times P \tag{10}\]  
In Equation (8), \(P\) denotes the pitch of a screw.  
It should be noted that if a target structure includes different types of threaded components, disassembly can be realized using a combination of the two following techniques: fuzzy decision, which is introduced for the adaptive determination of the screw pitch according to the vision measurement result and applicable conditions, and an advanced unfastening tool, which is designed to be applicable to screws with a wide size range.  
The rotational angle of the unfastening tool can be determined based on the distance from _surface_\(A\) to _surface_\(B\), which can be estimated based on values of heights \(Z_{c}\) and \(Z_{s}\), as shown in Figure 18. The length \(L_{s}\) of the engaged thread can be calculated by \(L_{s}=L-(Z_{c}-Z_{s})\), where \(L\) denotes the total length of a screw. To ensure the complete removal of the screw, the unfastening angle \(\theta_{t}\) of the tool can be determined by  
\[\theta_{t}=L_{s}/P\ \times\ 360+\theta_{s} \tag{11}\]  
where \(\theta_{s}\) is the safety rotational angle of the unfastening tool, which represents the increased angle based on the calculated angle determined by the cooperated motion planning of the robot and the unfastening tool. The definition angle \(\theta_{s}\) aims to ensure complete screw disassembly. In this work, the value of \(\theta_{s}\) is set to 960 deg, which means the unfastening tool will rotate three more times after the cooperated motion. Based on the experimental test results, the assembly reliability can be improved based on this strategy.  
The rotational orientation of the disassembly screw can be determined based on the screw thread rotational direction, including the left-handed and right-handed cases. In most applicable cases, screws with the same rotational direction are used. Most industrial applications use right-handed screws, which are also used in this work.