## 2 Finite Element Analysis of Proposed Shape
Figure 4 shows the comparative results of the displacements at the same applied force (35 N) for the three materials used in the study, clearly observing the much higher degree of deformation of the compliant mechanism of TPU, especially due to its mechanical properties being much more suitable for this application. Therefore, for the same applied force of 35 N, a maximum aperture of 27.86 mm is obtained for TPU (which corresponds to the real displacement range for the application of the compliant mechanism), a much higher value compared to those obtained for ABS and PLA--9.74 mm and 7.17 mm, respectively. Table 3 shows the simulation results obtained for the three materials studied in a certain force range (5-35 N) for the equivalent Von Mises stresses and the maximum openings of the compliant mechanism. It can be seen from the table, that at applied forces greater than 25 N, for ABS, the Von Mises stresses exceed the material yield limit, which indicates possible plastic deformation in some areas where this value is exceeded; an undesirable aspect for the application of the compliant mechanism. Figure 2: Some steps of FEM simulation of the TPU compliant mechanism at 35 N applied force: (**a**)-geometry model designing; (**b**)-fixing geometry, applying force and meshing; (**c**)-displacement results (undeformed model); (**d**)-displacement results (deformed model); (**e**)-Von Mises stress results; (**f**)-strain results (the arrows represent the mode of action of the force). Figure 5 shows the comparative results of the displacements of the fastening elements obtained according to the force for all three studied materials, where the much higher values for TPU of the displacements at the same applied force compared to acrylonitrile butadiene styrene and polylactic acid are clearly highlighted, to conclude that this material seems to be the most suitable candidate for the realization of the fastening systems applied in the field of clinical optometry discussed in this paper. This is due to its special mechanical properties that are manifested by increased elasticity and other important properties that recommend it for this application in the field of optometry. Between PLA and ABS, the former proved to have more suitable properties after simulation tests. Figure 3: Comparison of obtained mechanical characteristics results for three investigated materials (35 N applied force in all cases): (**a**)-TPU mechanism Von [PERSON] stress results; (**b**)-TPU mechanism displacement results between gripping elements; (**c**)-ABS mechanism Von [PERSON] stress results; (**d**)-ABS mechanism displacement results between gripping elements; (**e**)-PLA mechanism Von [PERSON] stress results; (**f**)-PLA mechanism displacement results between gripping elements. Figure 4: Comparison of resulted displacement and degree deformation at the same applied force-35 N for all investigated materials. Figure 5: Comparison of force-displacement characteristics for investigated materials. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**TPU (\(\sigma_{y}\) = 65.85 MPa)**} & \multicolumn{2}{c}{**ABS (\(\sigma_{y}\) = 45 MPa)**} & \multicolumn{2}{c}{**PLA (\(\sigma_{y}\) = 70 MPa)**} \\ \cline{2-7}
**F (N)** & \(\mathbf{y_{max}}\) [mm] & \(\mathbf{\sigma_{max}}\) [MPa] & \(\mathbf{y_{max}}\) [mm] & \(\mathbf{\sigma_{max}}\) [MPa] & \(\mathbf{y_{max}}\) [mm] & \(\mathbf{\sigma_{max}}\) [MPa] \\ \hline
5 & 4.03 & 8.4 & 1.35 & 8.35 & 1.03 & 8.3 \\ \hline
10 & 8.16 & 17.16 & 2.72 & 16.84 & 2.01 & 16.72 \\ \hline
15 & 12.32 & 26.11 & 4.11 & 25.47 & 3.03 & 25.25 \\ \hline
20 & 16.42 & 35.07 & 5.51 & 34.21 & 4.05 & 33.87 \\ \hline
25 & 20.4 & 43.87 & 6.91 & 43.05 & 5.09 & 42.58 \\ \hline
30 & 24.23 & 52.45 & 8.32 & 51.96 & 6.12 & 51.36 \\ \hline
35 & 27.86 & 60.68 & 9.74 & 60.93 & 7.17 & 60.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Obtained results for Von Mises stress and displacement between gripping elements.