# _Skin Imaging_: A Digital Twin for Geometric Deviations on Manufactured Surfaces
## 5 Experimental Results and Discussion
### Skin Imaging of the Case Studies  
Figure 13 shows a defective gudgeon pin, from which a set of PC data is acquired by a laser scanner. The imperfections are labeled on the figure. The best fitted cylinder (SG estimation step) to its PC is displayed in red color in Figure 14, both in the scanner coordinate system and SG coordinate system. Moreover, its PC in SG coordinate frame is shown in different views. As is clear, the fitted cylinder axis is obtained totally parallel with the \(\mathrm{X_{SG}}\), while the axis of PC's original coordinate system, i.e., scanner coordinate frame was not. This again demonstrates the efficiency of the modification step in SG estimation of the cylindrical surfaces discussed in Section 3.1.  
Figure 13: Defective gudgeon pin.  
Conducting the procedure discussed in Sections 3.2-3.4, the Deviation-Coordinate system for the gudgeon pin surface is generated (Figure 15a). Consequently, by applying the steps II and III of the _skin imaging_ methodology (Section 2), the _skin image_ of the scanned gudgeon pin is obtained (Figure 15b), which can be more processed to extract useful information about the surface deviation and therefore the manufacturing process that will be more discussed in the Section 5.2.  
For more clarification of the implementation of _skin imaging_ methodology on spherical surfaces, which has been discussed in Section 4, a spherical shape with a wavy surface is made (Figure 16a), from which a set of PC data is extracted. By fitting SG to its PC (Figure 16b), the Deviation-Coordinate system for its upper hemisphere is illustrated in Figures 16c and 16d in the 3D view and X-Y view, respectively. The waviness of the sphere surface is completely clear on the generated Deviation-Plane. Afterwards the _skin image_ of the upper hemisphere of this surface is generated, which is shown in Figure 17. Notably, for spherical _skin image_, there are four corners on the image, called void parts that are added just for completeness of the image and these parts are considered as the background and will not affect the surface inspection procedure.  
Figure 14: SG estimation for PC of gudgeon pin surface.  
Figure 15: (**a**) Deviation-Coordinate system, (**b**) skin image of the measured gudgeon pin.  
As an industrial spherical surface, the PC of a defective suspension ball joint (Figure 18) is imported to the proposed system. After fitting the best spherical to the captured PC, some (virtual) points that are located on the fitted ideal sphere are added to the measured PC in order to fill the two sections on the surface that actually have not been designed to be manufactured in spherical shape. Then all points are mapped to the SG coordinate system. As is shown in Figure 19, the sphere is divided into two hemispheres with X\({}_{\text{SC}}\)-Y\({}_{\text{SG}}\) plane, and the Deviation-Plane and Deviation-Coordinate system are generated for each hemisphere. Figure 20 presents the _skin image_ of both hemispheres together with their points in the X\({}_{\text{DCS}}\)-Y\({}_{\text{DCS}}\) view.  
Figure 16: **(a)** Model of the wavy sphere, **(b)** Its PC and fitted SG, **(c)** Deviation-Coordinate system for a wavy spherical surface (upper hemisphere) **(d)** Deviation-Coordinate system in X-Y plane.  
Figure 17: Skin image of the wavy spherical.  
Figure 19: SG estimation and Deviation-Coordinate system generation for the ball joint.  
Figure 18: Defective suspension ball joint (labels are the number of the defects).  
Figure 20: Skin images of the ball joint’s hemispheres.