## 3 Finite Element Method  
The Finite Element Method (FEM) was used as the basic tool for the analysis of compliant fingers [12; 18]. Through the numerical solution of mathematical equations, an iterative process simulates the investigated type of mechanisms, otherwise known as Finite Element Analysis (FEA). The ANSYS software package uses this approach for the detailed analysis of the structures under investigation and was used for the analysis in this paper. Simulation and analysis were performed in ANSYS version 19.2 [29]; for them to produce valid results that can be compared with the obtained experimental results, it is necessary to fully define the given compliant mechanism. Given that compliant mechanisms dimensions are already provided as an input parameter, it is now necessary to define the material from which the compliant mechanism is constructed. For these purposes, Fused Deposition Modeling (FDM) 3D printing of Nylon material was used to create prototypes of compliant fingers. The specifications of Taulman Nylon 230 obtained from the manufacturer can be seen in Table 1[30], and the 3D-printing process itself is described in the following.  
Taulman Nylon 230 is a perfect option given its flexibility-to-strength ratio. With this nylon used in 3D printing, there is no snapping or brittle effect, and the parts produced are very tough, durable, and resilient. In contrast to that, the thinner sections of the 3D-printed nylon can become highly flexible. Hence, Taulman Nylon 230 is perfect for the production  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Material Property** & **Taulman Nylon 230** \\ \hline Young’s modulus, E & 73 MPa \\ Poisson’s ratio, \(\
u\) & 0.39 \\ Ultimate tensile strength, \(\sigma_{\max}\) & 34 MPa \\ Ultimate elongation, \(\epsilon_{\max}\) & 417\% \\ Density, \(\rho\) & 1.14 g/cc \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mechanical properties of the 3D-printed Taulman Nylon 230.  
Figure 5: Compliant finger: (**a**) Curved flexure hinge with a \(\alpha_{1}=21\)-degree bend and (**b**) Curved flexure hinge with a \(\alpha_{2}=90\)-degree bend.  
of compliant mechanisms prototypes and the end-use flexure components. The next step is the detailed definition of the static and dynamic characteristics given by the real conditions under which the experiment will be performed.  
Figure 6 shows the defined boundary condition (fixed support A) and the load force (vector B defined in the negative direction of the horizontal axis) acting on the end of both compliant mechanisms with a 21-degree bend curved flexure hinge (Figure 6a) and a 90-degree bend curved flexure hinge (Figure 6b).  
It is also necessary to generate a finite element mesh and its goodness is an important factor for a successful analysis. At the locations of the flexure hinges, a mesh of finite elements is produced using the \"Face Meshing\" function to meet the correctness of the FEA results. A complete mesh is defined with quadrilateral components of size of 0.8 mm for rigid segments of compliant mechanisms and 0.2 mm for elastic segments (flexure hinge). For a compliant mechanism with a curved flexure hinge with a 21-degree bend, the resulting mesh of the FE model contained 2298 elements and 7307 nodes, while for a compliant mechanism with a 90-degree bend, it contained 2343 elements and 7478 nodes. Non-linear FEM analysis is considered in the simulation since the static analysis takes large deflection into account. Simulation parameters maximal bending angle, and maximal strain  
Figure 6: Boundary conditions and finite element mesh, maximal bending angle, and maximal strain of: (**a**) Curved flexure hinge with a 21-degree bend and (**b**) Curved flexure hinge with a 90-degree bend.  
are output parameters of interest, the results of which, in the case of maximum load force, can be seen in Figure 6.