# Stress Dispersion Design in Continuum Compliant Structure toward Multi-DOF Endoluminal Forceps
## 3 Evaluation
### Finite Element Analysis  
FEA was used to quantitatively evaluate the stress distribution to analyze whether a reduction in the stress concentration was achieved. Initially, we determined the material and FEA conditions. Polymer materials can be mass-produced at a low cost and discarded after one-time use. PAI (Polyamide-imide) is a biocompatible material with a low Young's modulus and yield strength among similar polymer materials [24]. Therefore, PAI is suitable as a material for the hinge of the forceps. In particular, FEMAP (SIEMENS PLM, Stuttgart, Germany) was used to generate the mesh considering tetrahedral elements. The analyses were conducted using the nonlinear numerical-analysis software DAFUL (Virtual Motion, Seoul, Korea). Table 2 shows the physical properties of PAI and the mesh size used for FEA. To be able to operate the forceps like a human wrist, the required range of motion is \(\pm\)90 degrees. Therefore, the force applied until the forceps bent 90 degrees in FEA. The FEA considered that the tensile force was always perpendicular to the tip of the surface each time the tip bent. First, a simulation was performed where a wire was pulled and bent in a lateral direction. Subsequently, a simulation was performed where two wires were pulled and bent in an oblique direction. The analysis conditions were set so that the tensions of the two wires were equal. To show the effectiveness of the improved design with a variable hinge thickness, we compared it to an initial design with a constant hinge thickness. For the design used for comparison, only the hinge size was changed, and the other parameters were maintained of the same size. The hinge thickness of the initial design was 0.35 mm. The FEA results when the hinge length was 0.4 mm are shown in Figure 5. Figure 6 shows the evenly distributed stress when the hinge length was 0.4 mm. When the tip was bent 90 degrees, the maximum stress of the initial design and improved design was 245 MPa and 148 MPa, respectively. Consequently, the maximum stress is smaller than the yield strength of PAI. The improved design allowed stress dis \begin{table}
\begin{tabular}{l l} \hline \hline
**Material Property** & **Value** \\ \hline Young’s modulus & 4000 (MPa) \\ Shearing modulus & 1379 (MPa) \\ Yield strength & 152 (MPa) \\ Poisson ratio & 0.45 \\ Mesh size & 0.15 (mm) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material properties and mesh size considered in the FEA. Figure 4: Diagram of the forceps when the hinge length was 0.4 mm: (**a**) initial design and (**b**) improved design. stress was substantially reduced compared to that of the initial design. Figure 7 shows the results of comparing the maximum stresses when FEA is performed using different hinge lengths. For all hinge lengths, the improved design significantly reduced the maximum stress compared to the initial design. However, the maximum bending stresses of the initial design and the improved design are larger than the yield stress of PAI when pulling with two wires. Therefore, the angle at the maximum bending stress that does not exceed the yield stress is defined as the maximum bending angle, as shown in Figure 7. The bending range of the improved design was larger than that of the initial design. Note that the average analysis time for non-linear analysis using FEA required approximately 4800 s on a computer with an Intel Xeon W-3235 Dodeca-core 3.30 GHz, using 192 GB of RAM. The proposed method can derive parameters in almost real time, even using versatile numerical calculation software. Thus, the proposed method obtained the design parameters with a lower computational cost than the design method of previous research using FEA [24; 25; 26; 27]. The results show the effectiveness of the proposed design method for successful motion generation. Figure 5: FEA results when the hinge length was 0.4 mm: (**a**) initial design and (**b**) improved design. Figure 6: Distribution of maximum stress for each segment when the hinge length was 0.4 mm.