## 2 Finite Element Analysis of Proposed Shape  
In order to predict the displacement of the proposed system and, in this sense, to choose the optimal material to realize the physical model for the given application, the designed structures were simulated using the finite element method, starting with three materials frequently used in FDM technology. With the help of finite element method analysis, the 3D model was simulated assuming that it was divided into several smaller elements, with their size and number depending on the fineness of the meshing. Exact numerical models should predict the mechanical behaviour of an investigated structure, but in most cases these models must be validated. To be confirmed first, the correct geometry and the corresponding characteristics of the materials used are required. Furthermore, the exactness of the values obtained by the finite element method analysis depends to a large extent on the fineness of the measurement and discretization parameters, but, at the same time, it also depends on the correct application of mechanical loads. The combination of Finite Element Analysis FEA with experimental validation of the mechanical behaviour of the compliant mechanisms investigated can be considered the most appropriate way to study, compare, and choose the optimal materials and/or manufacturing technologies for this application, and when the results of numerical and experimental methods are close, the developed structure can be validated. In this FEM study, three thermoplastic materials were used that could be possible candidates for the marker clamp systems used in the optometric field--acrylonitrile butadiene styrene (ABS) [24; 25; 26; 27], polylactic acid (PLA) [28; 29; 30; 31], and thermoplastic polyurethane (TPU) [32; 33; 34; 35], and as a medium, SolidWorks was used for the simulation. The main mechanical properties for the materials used in the study are represented in Table 2[36; 37; 38], which are essential elements for the correctness of the results obtained by Finite Element Method FEM analysis. The main steps for performing the numerical simulation can be highlighted are the application of the material, the definition of the fixed geometries, the application of the loads, and their division into finite elements--the meshing. The following measurement parameters were used in this study:  
- Mesh type: Solid Mesh  
- Element Size: 1.43838 mm  
- Tolerance: 0.0719189 mm  
- Mesh Quality: High  
- Total Nodes: 15,490  
- Total Elements: 8368  
- Maximum Aspect Ratio: 13,989  
- % of elements with Aspect Ratio < 3: 96.5  
- % of elements with Aspect Ratio > 10: 0.0956  
- % of distorted elements (Jacobian): 0  
Figure 2 shows some simulation steps and the results obtained for TPU when applying a force of 35 N, also observing the way in which the structure is deformed. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Property** & **ABS** & **PLA** & **TPU** \\ \hline Density & 1.02 g/cm\({}^{3}\) & 1.252 g/cm\({}^{3}\) & 1.18 g/cm\({}^{3}\) \\ Young Modulus & 1.18 GPa & 1.59 GPa & 0.396 GPa \\ Poisson ratio & 0.35 & 0.36 & 0.3897 \\ Yield strength & 45 MPa & 70 MPa & 65.85 MPa \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Properties of materials used in the study. Figure 3 shows the results obtained for the mechanical characteristics of interest: the equivalent Von Mises stresses and the maximum opening or distance/displacement obtained between the two fastening elements. The Von Mises stresses obtained for all three investigated materials are presented in Figure 3a,c,e, and it can be observed that for the ABS material the value of Von Mises stress at 35 N exceeds the yield strength of the material. To obtain the results of the maximum opening of the compliant mechanism as a result of applying the request, it was set from SW to only display the results of the entities of interest, as shown in Figure 3b,d,f, the total distance obtained by summing the resulting displacements of the two clamping elements.