## 5 Implementation and Examples
### Example Verification
#### 5.2.3 Automatic Screening of AT Types  
1. Constructing the set of tolerance type assertions TABOX for each assembly face of Part\({}_{3}\). According to the reasoning in Section 5.2.2, the tolerance types of each AFS P\({}_{3}\)SF\({}_{1}\), P\({}_{3}\)SF\({}_{2}\), P\({}_{3}\)SF\({}_{3}\), and P\({}_{3}\)SF\({}_{4}\) of part Part\({}_{3}\) were obtained. The selection tolerance type assertion set As was constructed, as represented by Equation (8). TAs = [Perpendicularity(Per3_1), Perpendicularity(Per3_2), Perpendicularity(Per3_3),  
Perpendicularity(Per3_1), Cylindricity(Gly3_1), Cylindricity(Gly3_2), Cylindricity(Gly3_3),  
Flatness(Fla3_4), Roundness(Rou3_1), Roundness(Rou3_2), Roundness(Rou3_3),  
Straightness(Str3_1), Straightness(Str3_2), Straightness(Str3_3), Straightness(Str3_4),  
CircularRunOut(CirRunOut3_2), CircularRunOut(CirRunOut3_3), CircularRunOut(CirRunOut3_4),  
TotalRunOut(ToRunOut3_2), TotalRunOut(ToRunOut3_3), TotalRunOut(ToRunOut3_4),  
Coaxianlity(Coa3_1), Coaxianlity(Coa3_2), Coaxianlity(Coa3_3),  
AixStraightness(AixStr3_1), AixStraightness(AixStr3_2), AixStraightness(AixStr3_3),  
Position(Pos3_1), Position(Pos3_2), Position(Pos3_3), Position(Pos3_4)]. 2. Setting of the control parameters DOF vector \(\mathbf{V}_{0}\). Based on the geometric functional requirements of the assembly and the coordinate system determined in step 2 of Section 5.2.1, we instantiated tolerance-zone DOFs under the DOF class in the tolerance specification design knowledge ontology library. Based on this, the common parameter DOF determination rule and the control parameter DOF determination rule  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**ASF 1**} & \multicolumn{3}{c}{**—**} & \multicolumn{3}{c}{**—**} & \multirow{3}{*}{\(\bigcirc\)**} & \multirow{3}{*}{\(\bigcirc\)**} & \multirow{3}{*}{\(\bigcirc\)**} & \multirow{3}{*}{\(\bigcirc\)**} & \multirow{3}{*}{\(\bigcirc\)**} & \multirow{3}{*}{\(\bigcirc\)**} & \multirow{3}{*}{\(\bigcirc\)**} & \multirow{3}{*}{\(\bigcirc\)**} & \multirow{3}{*}{\(\bigcirc\)**} & \multirow{3}{*}{\(\bigcirc\)**} & \multirow{3}{*}{\(\bigcirc\)**} \\ \cline{3-3} \cline{8-11}  & **In the** & **In Any** & & & & & & & & & & \\ \cline{1-1} \cline{6-11}  & & **Plan** & **Direction** & & & & & & & & & \\ \hline \multirow{4}{*}{Recommended tolerances} & P\({}_{3}\)S\({}_{1}\) & & & \(\surd\) & \(\surd\) & \(\surd\) & & & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \\ \cline{1-1} \cline{6-11}  & P\({}_{3}\)S\({}_{2}\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \\ \cline{1-1} \cline{6-11}  & P\({}_{3}\)S\({}_{3}\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \\ \cline{1-1} \cline{6-11}  & P\({}_{3}\)S\({}_{4}\) & \(\surd\) & & & \(\surd\) & \(\surd\) & \(\surd\) & \proposed in Section 4.5.2 were combined to infer the control parameter DOF vector \(V_{0}\) (the instantiation name is represented by CPDF). The data properties of instance CPDF are shown in Figure 14. The control parameter DOF vector \(V_{0}\) = (0 0 0 1 1 0) can be obtained from the data attributes of CPDF. 3. Determination of comparative DOFs for different tolerance types. Using the comparative DOF calculation inference rule proposed in Section 4.5.2, the comparative DOFs for the different tolerance types on the AFSs of the work piece Part\({}_{3}\) were inferred. The AFS P\({}_{3}\)S\({}_{1}\) of the work piece Part\({}_{3}\) had multiple recommended tolerance types, and coaxiality tolerance was one of them. Example B_Coa3 is the comparative DOF for instance Coa3. After reasoning through the SWRL rule for comparing DOFs, the attribute values of the B_Coa3_1 instance were obtained, as shown in Figure 15.
4. Screening of tolerance types.