## 3 Results and Discussion  
### Automation of the Scanning Procedure  
If the process of scanning has to be repeated multiple times and/or on multiple samples, a good time-saving solution would be to design a mechanical arm which can follow a programed path with a structured light scanner attached to the end point of the mechanism. A schematic of the scanning path is given in Figure 7.  
The program is designed in such a way that the path composed of straight lines and arcs of circles is approximated by a set of points along this path linked with segments of a line of length given by an allowed approximation error. Based on automated scanning with a 3D handheld scanner for the mechanical properties of the footwear scanned for finite element and thermal analysis in order to identify  
Figure 6: VX scan processing of shoe type B to obtain a 3D model. Figure 7: Scanning path in case of automated scanning with 3D handheld scanner: (**A**) scanning path for footwear type A used for indoor sport, (**B**) scanning path for footwear type B used for indoor sport. the areas that provide the best foot ventilation for comfort in movement, are going to be presented in a future paper. Figure 8 shows the forward kinematic schematics used to automate the scanning process using a 3D handheld scanner. In order to obtain automated scanning of a product we could use a robotic arm but this is not economically feasible. In our opinion, it is better to have a robot-like arm with three degrees of mobility (three actuated joints) which can be controlled by a simple and non-expensive controller. The mechanical arm would have a planar motion to follow the path (like the one described in Figure 7) and in order to scan different sides of the object we can rotate the object (for example to scan the lateral side of the shoe). A diagram of such a device is given in Figure 8. In order to control the movement of the scanner on a prescribed path, the program will need to be written by developing the forward and reverted kinematics of the device. We assume that point C of the device has to reach consecutive points of the path--in Figure 8, the second quadrant of circle M, which is part of the scanning path. There is also a constraint that the l\({}_{3}\) segment of the arm has to be perpendicular on the tangent to the circle, so having the same orientation as the radius from point M to point C, defined by angle \(\alpha\). The perpendicularity constraint is given by the requirement that the scanner is attached to the l\({}_{3}\) segment with the scanning of the structured light the same orientation as the l\({}_{3}\) segment. If the path is a straight line, angle \(\alpha\) is or the line's slope. Then we can define angle \(\alpha\) in accordance with angle \(\delta\) which is the usual trigonometric orientation of the radius defined by points M and C, describe in Equation (1) as follows:  
\[\alpha=\pi-\delta \tag{1}\]  
Next is described the development of basic relations of the forward and inverse kinematics of the device. In forward kinematics the goal is to obtain the coordinates \(y_{\rm C}\) and \(z_{\rm C}\) when \(\theta_{1}\), \(\theta_{2}\), and \(\theta_{3}\) are known. Using the notations in Figure 8, we can infer the values of the coordinates of point C as follows:  
We can write angle \(\alpha\) as a function of the known angles describe in Equations (2) and (3) as follows:  
\[\theta_{1}-\theta_{2}=\theta_{3}-\alpha \tag{2}\]  
\[\theta_{3}+\theta_{2}-\theta_{1}=\alpha \tag{3}\]  
Figure 8: Forward kinematic schematics for automated scanning with a 3D handheld scanner. Equations (4) and (5) describe the coordinates of point B in terms of the length \(l_{1}\) and angle \(\theta_{1}\). \[y_{B}=\ 1_{1}\cos\theta_{1} \tag{4}\]  
\[z_{B}=l_{1}\sin\theta_{1} \tag{5}\]  
Equations (6) and (7) represent the distances DB and AD in terms of the length \(l_{2}\) and the difference between angles \(\theta_{1}\) and \(\theta_{2}\).