## 3 Methods for Analyzing the Disassembly Process
### Fourth Method  
The fourth and last method was proposed by [PERSON], [PERSON], [PERSON], and [PERSON] in the work entitled \"Selective disassembly sequence generation based on lowest level disassembly graph method\" [12].  
Two graphs are used, the DGCG (disassembly geometry contacting graph) and the DOG (disassembly order graph), where, in the first graph, the components participating in general operation are divided into different levels depending on the order of removal, identifying the components with circles and the fasteners with rectangles. To build the DGCG, however, it is necessary to make an accurate study of the CAD model designed to verify that there are no collisions between the projections of parts: \"geometric feasibility\" and \"collision detection\". The first refers to two components that can be assembled/disassembled without causing collisions with each other in order to find the direction and the disassembly path. Instead, to analyze the collisions that occur during disassembly, the \"project calculation\" proposed by [PERSON] is used, which consists of projecting the volume of the target component in a chosen direction (2D); if no collisions are found, then it is defined as direction-correct because the basic principle is that if a collision occurs at the 2D level, then it certainly occurs at the volume level as well. When a part can be removed without requiring the extraction of other parts, it is placed in the first level called _1-st-disassembly-level_. Otherwise, it is placed in other lower levels after specifying, for each higher level, the reason for its inability to be removed using the abbreviations: C\({}_{\text{n}}\)\({}^{\text{ij}}\) refers to a level n where component \(i\) cannot be disassembled due to a collision with component \(j\); N\({}_{\text{Sn}}\)\({}^{\text{1}}\) refers to when component i cannot be removed at level n due to the absence of a SDR (set of directions for removal); the second graph is a graphic representation of the path that has been chosen to reach the target component. Therefore, the sequence is built starting from the first level and then descending, releasing the components placed below each time.  
Application of the Fourth Method  
To use this method, it was decided that we must consider several assemblies of components: S1 = [13, 12], S2 = {4, 2-3 SX}, S3 = {1-14, 2-3 DX}, S4 = {10, 7 SX}, S5 = {10, 7 DX}, and the 5 SX and 5 DX pins as if they were welded to the hydraulic pump body since they do not participate in disassembly and, in fact, do not hinder other components in their removal. The target component remains the drive gear. The first level of the DGCG (Figure 10) is composed entirely of fasteners, as is more generally the case because they are usually free to be removed immediately from the product.  
Figure 10: Disassembly geometry contacting graph (DGCG).  
Two possible disassembly sequences are obtained, visible in the following DOGs (Figure 11a,b):  
* Seq. 1: S1, 11, S2, S4, 9;
* Seq. 2: S1, 15, 16, 11, S3, S5, 9.  
The optimal sequence is the first one. By breaking down the subassemblies defined at the start, we obtain, in BOM codes: 16, 13, 12, 11, 4, 2-3 SX, 10-7 SX, 9.