## 3 Finite Element Analysis (FEA) Validation  
Following the design of the mechanism, the design was modeled to verify the designed mechanism and its performance in terms of stress analysis under the applied force. For this purpose, a finite element analysis (FEA) was performed using Autodesk Inventor Professional 2021 software. The device was modeled according to the details and specifications of the design. The specifications and the architectural design of the designed distractor are presented in Table 1 and Figure 6.  
Figure 5: Design of the FCC.  
The stiffness is an essential factor in the FEA of the distractor which is defined by dividing the input load by the corresponding displacement of the input end of the mechanism. The effect of applying an external force on the surface strain of the distractor is simulated and analyzed, which can indicate the effect of applying external forces to the distraction zone and the distractor. The results of the analysis are presented in Figures 7-9. According to the literature, during the reconstruction process, a maximum peak of 200 N is applied to the healing zone when the patient is biting or eating on a normal occasion [42]. Therefore, in the mechanical analysis of the distractor, a pushing force of 300 N was applied to the mechanical fixtures of the distractor. A maximum pushing force of 50 N was applied to each mechanical fixture in six points. Stainless-steel material with a mass density of 8 gr/cm\({}^{3}\), yield strength of 250 MPa, ultimate tensile strength of 540 MPa, Young's modulus of 193 GPa, Poisson's ratio of 0.3 \(\mu\)L, and shear modulus of 74.23 GPa was selected as the material in the stress analysis. Simulation results show that the designed device has a total mass of 0.268 kg with a total volume of 33,509 mm\({}^{3}\). The selected material is biocompatible and an ideal choice for manufacturing the distractor.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Symbol** & **D1** & **D2** & **D3** & **D4** & **D5** & **D6** & **D7** & **D8** & **D9** \\ \hline Value (mm) & 10 & 55 & 35 & 55 & 30 & 30 & 30 & 6 & 6 \\ \hline Symbol & D10 & D11 & D12 & D13 & D14 & D15 & D16 & D17 & D18 \\ \hline Value (mm) & 26 & 6 & 6 & 14 & 46 & 4.5 & 40.5 & 6.8 & 10.7 \\ \hline Symbol & D19 & D20 & D21 & D22 & D23 & D24 & D25 & D26 & D27 \\ \hline Value (mm) & 30 & 31 & 14 & 40 & 11 & 11 & 11 & 11 & 11 \\ \hline Symbol & D28 & D29 & D30 & D31 & D32 & D33 & D34 & D35 & D36 \\ \hline Value (mm) & 50 & 4 & 4 & 4.5 & 5 & 8 & 13.5 & 8 & 8.5 \\ \hline Symbol & D37 & D38 & D39 & D40 & D41 & D42 & D43 & D44 & D45 \\ \hline Value (mm) & 15 & 3.7 & 5.5 & 2 & 3 & 2.5 & 6 & 2.5 & 2 \\ \hline \end{tabular}
\end{table}
Table 1: Architectural parameters of the designed passive distractor.  
Figure 6: Architectural parameters of the designed distractor.  
Figure 7 illustrates the Von Mises Stress analysis of the distractor. It can be seen that a maximum Von Mises Stress of 77.56 MPa is applied to the mechanical fixture when the device is under a pushing force of 300 N. Figure 8 illustrates the 1 st Principal Stress analysis of the distractor. It can be seen in Figure 7 that a maximum stress of 81.51 MPa is applied to the mechanical fixtures when a pushing force of 300 N is applied to the distractor. Figure 9 illustrates the displacement of the designed distractor under the applied forces, with a maximum displacement of 4 um under the applied force. It can be deduced from the FEA results that in all conditions, the designed mechanism has high strength with a minimum safety factor of 5.13 uL which guarantees good positioning accuracy, repeatability, and linearity of the distractor during the activation phase of the DO process.  
Figure 8: 1 st Principal Stress analysis of the designed distractor.  
Figure 7: Von Mises Stress analysis of the designed distractor.