## 3 Results and Discussion
### Displacement Results  
In Figure 12, the most significant displacement is marked in red. This displacement is excluded from consideration because this section of the load holder serves as a platform for the human loading of 1200 N. The red-highlighted corner is positioned farthest from the center of the rod. As the rod rotates under torque, frictional contact with the load holder causes it to move. Consequently, the corners experience the greatest displacement. Table 7 reveals a notable trend in the total displacement values (rounded off to 3 s.f. ), showcasing that Titanium Commercial Purity Grade 4 (annealed) exhibits the highest displacement among all pitches and engagement threads. Following closely is the Stainless Steel Austenitic AISI 316L (annealed), which exhibits the least total displacement. This observation highlights the distinct mechanical behaviors of these materials under the given conditions, with Titanium Commercial Purity Grade 4 showcasing the most significant displacement, Titanium Alpha-Beta Alloy Ti-6 Al-4V displaying an intermediate response,  
Figure 11: The 20-thread engagement, stress vs. pitch. Figure 12: (**a**) Displacement simulated diagram; and (**b**) displacement location. and Stainless Steel Austenitic AISI 316L demonstrating the least total displacement. Understanding these displacement patterns is crucial for optimizing the selection of materials based on specific project requirements, ensuring structural stability and performance in various applications. For Figures 13 and 14, data analysis reveals that Titanium Commercial Purity Grade 4 (annealed) demonstrates the highest displacement among the three types of engagement threads. The impact of material strength becomes notably significant, with Titanium Commercial Purity Grade 4 (annealed) displaying the most substantial displacement under a torque load of 1.1 N-m. This highlights the pivotal role of material strength in determining the response to applied torque, showcasing both the robustness and susceptibility to deformation of Titanium Commercial Purity Grade 4 (annealed) under the specified torque conditions, despite exhibiting the best results. However, considering the risk of stress exceeding the lower limit, it may not be the optimal material choice in this scenario. Additionally, the data illustrate a clear trend where displacement decreases with an increase in thread engagement. This trend is attributed to the reduced contact area and friction due to torque with lower thread engagement, while higher thread engagement leads to an expanded contact area, increasing frictional force, and subsequently reducing displacement. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Pitch**} & \multirow{2}{*}{**Simulation**} & \multicolumn{3}{c}{**Total Displacement (mm)**} \\  & & **10 Thread** & **15 Thread** & **20 Thread** \\ \hline \multirow{3}{*}{0.25 mm} & Stainless steel austenitic AISI 316L (annealed) & 0.0336 & 0.0259 & 0.0131 \\  & Titanium commercial purity Grade 4 (annealed) & 0.0395 & 0.0278 & 0.0220 \\  & Titanium alpha beta alloy Ti-6 Al-4V (annealed) & 0.0337 & 0.0264 & 0.0208 \\ \hline \multirow{3}{*}{0.30 mm} & Stainless steel austenitic AISI 316L (annealed) & 0.0270 & 0.0191 & 0.0128 \\  & Titanium commercial purity Grade 4 (annealed) & 0.0464 & 0.0309 & 0.0206 \\  & Titanium alpha beta alloy Ti-6 Al-4V (annealed) & 0.0411 & 0.0276 & 0.0194 \\ \hline \multirow{3}{*}{0.35 mm} & Stainless steel austenitic AISI 316L (annealed) & 0.0246 & 0.0178 & 0.119 \\  & Titanium commercial purity Grade 4 (annealed) & 0.0415 & 0.0300 & 0.0185 \\  & Titanium alpha beta alloy Ti-6 Al-4V (annealed) & 0.0369 & 0.0264 & 0.0175 \\ \hline \multirow{3}{*}{0.40 mm} & Stainless steel austenitic AISI 316L (annealed) & 0.0213 & 0.0145 & 0.0101 \\  & Titanium commercial purity Grade 4 (annealed) & 0.0367 & 0.0251 & 0.0112 \\ \cline{1-1}  & Titanium alpha beta alloy Ti-6 Al-4V (annealed) & 0.0343 & 0.0155 & 0.0104 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Displacement simulation results.