# Spatial Data-Based Automatic and Quantitative Approach in Analyzing Maintenance Reachability
## 3 Materials and Methods
### Intersection Detection-Based Spatial Relationship Judgment between Arm and Product
#### 3.3.3 Intersection Detection Efficiency Test
\begin{table}
\begin{tabular}{l c c c c} \hline \hline \multicolumn{1}{c}{**Notesary Geometric Characteristic Data (mm)**} & \multicolumn{1}{c}{**Hand Coordinates**} \\ \cline{2-4}
**Objects to Be Tested** & **Position Class** & **Range Class** & **Direction Class** & **(mm)** \\ \hline \multicolumn{1}{c}{Object 1 (Sphere)} & (22.21, 999.09, 630.79) & 147.34 & \(-\) \\ \hline \multicolumn{1}{c}{Object 2 (Sphere)} & (515.04, 1.04, 471.33) & 126.01 & \(-\) \\ \hline \multicolumn{1}{c}{Object 3 (Sphere)} & (\(-\)65.00, \(-\)396.52, 169.93) & 147.69 & \(-\) \\ \hline \multicolumn{1}{c}{Object 4 (Sphere)} & (-57.83, 201.53, 339.40) & 103.68 & \(-\) \\ \hline \multicolumn{1}{c}{Object 5 (Sphere)} & (28.68, 200.57, 551.60) & 110.35 & \(-\) \\ \hline \multicolumn{1}{c}{Object 6 (Sphere)} & (\(-\)311.41, \(-\)97.50, 249.67) & 138.75 & \(-\) \\ \hline \multicolumn{1}{c}{Object 7 (Cylinder)} & (427.98, 581.87, \(-\)133.35) & (337.05, 394.31, 409.04) & 140.84 & \(-\) \\ \hline \multicolumn{1}{c}{Object 8 (Cylinder)} & (207.07, 43.46, \(-\)268.07) & (211.44, \(-\)153.20, 153.89) & 126.45 & \(-\) \\ \hline \multicolumn{1}{c}{Object 9 (Cylinder)} & (-\(\)221.13, 137.65, \(-\)350.12) & (-\(\)311.08, \(-\)49.97, 274.2) & 134.72 & \(-\) \\ \hline \multicolumn{1}{c}{Object 10 (Cylinder)} & (-\(\)1642.46, \(-\)94.97) & (\(-\)255.17, 497.60, 327.42) & 110.62 & \(-\) \\ \hline \multicolumn{1}{c}{Object 11 (Capsule)} & (81.90, 928.48, \(-\)111.01) & (674.73, 330.43, \(-\)270.48) & 127.16 & \(-\) \\ \hline \multicolumn{1}{c}{Object 12 (Capsule)} & (-\(\)398.14, 530.92, \(-\)412.41) & (94.69, \(-\)67.13, \(-\)571.87) & 135.13 & \(-\) \\ \hline \multicolumn{1}{c}{Object 13 (Capsule)} & (\(-\)108.12, 729.70, \(-\)261.71) & (984.71, 131.65, \(-\)422.18) & 147.82 & \(-\) \\ \hline \multicolumn{1}{c}{Object 14 (OBB)} & (102.05, 763.79, 259.89) & [133, 104.72, \(\surd\) & \(\surd\) (698.03, \(-\)3010.6547) \\ \multicolumn{1}{c}{Object 15 (OBB)} & (109.00) & & \(\surd\) (70.053, \(-\)030.007, \(-\)074.043) \\ \hline \multicolumn{1}{c}{Object 15 (OBB)} & (94.89, 165.74, 100.43) & [126.94, 143.88, \(\surd\) & \(\surd\) (70.954, 0.034, \(-\)0.6589) \\ \multicolumn{1}{c}{Object 16 (OBB)} & (94.89, 165.74, 100.43) & 146.31] & \(\surd\) (0.0391, 9945.0, 0.07924) \\ \multicolumn{1}{c}{Object 16 (OBB)} & (14.85, \(-\)231.83, \(-\)200.97) & [132.53, 100.72, \(\surd\) & \(\surd\) (908.191, \(-\)0.179, \(-\)0.2745) \\ \multicolumn{1}{c}{} & \(\surd\) (0.027, 0970.0, 0.2386) \\ \hline \multicolumn{1}{c}{Object 17 (OBB)} & (\(-\)477.99, 3662.2, \(-\)41.51) & [136.33, 114.72, \(\surd\) & \(\surd\) (0.0548, \(-\)0.016, \(0.8611)] \\ \multicolumn{1}{c}{} & \(\surd\) (70.954, \(-\)0.016, \(0.8611)] \\ \multicolumn{1}{c}{} & \(\surd\) (70.955, \(-\)0.067, \(-\)0.3723) \\ \hline \multicolumn{1}{c}{Object 18 (Irregular)} & P1 (25.02, \(-\)197.74, 300.88) & PS (183.55, \(-\)227.87, 320.63) & (P1, PS, PS, PS) (71.16, PS) & (P4, PS, PS, PS) \\ \multicolumn{1}{c}{Object Represented by 2} & P2 (276.26, \(-\)197.74, 300.36) & PS (240.86, \(-\)246.49, 320.63) & \(-\) & (P1, PS, PS, PS) \\ \multicolumn{1}{c}{Triangular Particles} & P3 (204.08, \(-\)148.93, 20.63) & PS (270.26, \(-\)276.74, 20.38) & (P1, PS, PS) & (P4, PS, PS) \\ \multicolumn{1}{c}{Object 19 (Irregular)} & P1 (25.871, \(-\)301.511, \(-\)67.65) & (\(-\)302.87, 400.38, \(-\)48.010) & (P1, PS, PS) & (P1, PS, PS, PS) \\ \multicolumn{1}{c}{Object 19 (Irregular)} & P2 (214.75, 400.31, \(-\)48.010) & PS (249.34, 334.84, \(-\)10.10) & \(-\) & (P1, PS, PS) \\ \multicolumn{1}{c}{Object Represented by 2} & P3 (241.28, \(-\)426.48, \(-\)48.010) & PS (\(-\)21.28, \(-\)34.34, \(-\)8.010) & (P1, PS, PS) & (P2, PS) & (P3, PS, PS) \\ \multicolumn{1}{c}{Triangular Particles} & P4 (294.34, 446.26, 480.10) & PS (\(-\)267.81, 400.31, 418.53) & (P1, PS, PS, PS) & (P2, PS) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Necessary Geometric Characteristic Data of the Object in Score 4. By processing the data in Table 8, the statistical parameters of the DOR under different division values can be obtained.