# Spatial Data-Based Automatic and Quantitative Approach in Analyzing Maintenance Reachability
## 5 Conclusions and Discussion  
In this study, an automatic and quantitative approach is proposed on the basis of human arm spatial data to conduct maintenance reachability. First, an arm model that considers kinematics is established to obtain the formulae of the joint positions in the hand coordinate system, then the initial solution set of the arm pose was generated by dividing the joint space. Second, to enhance the calculation efficiency, a 3D model reconstruction method is proposed. The reconstructed models are further parameterized for convenient calculation. Moreover, several intersection detection methods are adopted purposefully for various objects with different geometrical characteristics in the maintenance scene. Third, the impact of the two points above, namely, different joint range divisions and the intersection detection method selection on the efficiency, are analyzed. Fourth, in the analysis, the DOR is introduced to quantify the extent of reachability, and the impact of different joint range divisions on DOR are also analyzed. The conclusion of the analysis can be summarized as the intersection detection method efficiency ranges from high to low as the line segment and sphere, cylinder, OBB, triangular patch, and capsule. As the division value decreases, the efficiency increases rapidly and the division value has little effect on DOR. Lastly, four cases are selected to verify the methodology. The advantages of the proposed methodology can be expressed as follows. 1. All possible arm postures that are required to move freely are considered and transformed into an initial global dataset, whereas the subsequent analysis is conducted by starting from this initial global dataset. Consequently, the finitude occurring in the current methods can be reduced to some extent. 2. The determination of the initial global data set is also fully optimized and screened, which not only ensures the data of the arm are not lost, but also ensures the efficiency of the calculation process. 3. As the calculation process and resulting expression of reachability are quantitative, the judgments on whether the maintenance spot is reachable or not and how easy it is to reach have a lower dependence on a person. Hence, the proposed methodology is objective. 4. On the basis of quantitative analysis, the proposed can not only analyze the quality of accessibility design, but also show how good or how bad it is by means of quantitative expression. However, the proposed methodology requires improvements. Owing to the importance of the initial hand posture in the method, considerations on hand posture in maintenance should be covered. Future works will focus on this point to enhance the adaptability \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scene** & **Average Value** & **Variance** & **Standard Deviation** & **Variable Coefficient** \\ \hline Scene 1 & 0.66387750 & 0.00001798 & 0.00423992 & 0.00638660 \\ Scene 2 & 0.67263563 & 0.00000915 & 0.00302524 & 0.00449759 \\ Scene 3 & 0.17843125 & 0.00000302 & 0.00173703 & 0.00973501 \\ Scene 4 & 0.15127875 & 0.00000963 & 0.00310363 & 0.02051600 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Statistical Parameters of the DOR of Each Scene Obtained under Different Division Values.