# Amplification Ratio of a Recycled Plastics-Compliant Mechanism Flexure Hinge
## 3 Results and Discussion
### LDPE/TPU Blend Flexure Hinge  
In the previous section, the flexure hinges were produced with PP, ABS, and HDPE plastics. The recycle ratios of the PP, ABS, and HDPE plastics were also investigated. This section further investigates the LDPE blend flexure hinge, combining it with 0-25% \begin{table}
\begin{tabular}{c c c} \hline \hline
**Materials** & **Amplification Ratio** & **References** \\ \hline PP & 5.35 & This report \\ \hline ABS & 7.6 & This report \\ \hline HDPE & 5.02 & This report \\ \hline Aluminum alloys & 41 & [PERSON] et al. [31] \\ \hline Spring steel & 13–15 & [PERSON] et al. [32] \\ \hline Titanium alloys & 6.0 & [PERSON] et al. [33] \\ \hline Smart memory alloys & 2.2 & [PERSON] et al. [34] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Amplification ratios of different flexure hinge materials. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Recycle Ratio** & **PP** & **ABS** & **HDPE** \\ \hline
25\% & \(y_{1}=5.728x_{1}\) & \(y_{7}=8.249x_{7}\) & \(y_{13}=5.668x_{13}\) \\ \hline
20\% & \(y_{2}=5.50x_{2}\) & \(y_{8}=7.843x_{8}\) & \(y_{14}=5.404x_{14}\) \\ \hline
15\% & \(y_{3}=5.381x_{3}\) & \(y_{9}=7.646x_{9}\) & \(y_{15}=5.159x_{15}\) \\ \hline
10\% & \(y_{4}=5.288x_{4}\) & \(y_{10}=7.506x_{10}\) & \(y_{16}=4.852x_{16}\) \\ \hline
5\% & \(y_{5}=5.183x_{5}\) & \(y_{11}=7.233x_{11}\) & \(y_{17}=4.616x_{17}\) \\ \hline
0\% & \(y_{6}=5.036x_{6}\) & \(y_{12}=7.152x_{12}\) & \(y_{18}=4.436x_{18}\) \\ \hline Average ratio & 5.35 & 7.60 & 5.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Displacement equations of the PP, ABS, and HDPE plastics flexure hinge at different recycle ratios. TPU. As shown in Section 2, the LDPE polymer is weaker than all PP, ABS, and HDPE plastics. Therefore, adding the TPU could change the flexure hinges performance made from LDPE/TPU blend by enhancing the mechanical properties. Figure 7 displays the average displacement diagrams of LDPE blend flexure hinge at different TPU percentages. With the maximum input value of 95 \(\upmu\)m, the average output value is 947 \(\upmu\)m, indicating the high amplification rate of the hinge. The regression equations for the average values of the input and output displacements are as follows:  
\[y_{19}=2.853x_{19} \tag{19}\]  
\[y_{20}=4.517x_{20} \tag{20}\]  
\[y_{21}=6.323x_{21} \tag{21}\]  
\[y_{22}=9.376x_{22} \tag{22}\]  
\[y_{23}=10.37x_{23} \tag{23}\]  
\[y_{24}=10.504x_{24} \tag{24}\]  
where \(y_{19}\), \(y_{20}\), \(y_{21}\), \(y_{22}\), \(y_{23}\), and \(y_{24}\) are the output data; and \(x_{19}\), \(x_{20}\), \(x_{21}\), \(x_{22}\), \(x_{23}\), and \(x_{24}\) are the input data of the LDPE/TPU blend flexure hinge at TPU percentages of 0%, 5%, 10%, 15%, 20%, and 25%. Improving the input value mostly leads to a linear increase in the output value. The amplification ratio values are 2.85, 4.517, 6.323, 9.376, 10.37, and 10.504, corresponding to the LDPE/TPU blend flexure hinge at 0%, 5%, 10%, 15%, 20%, and 25% TPU percentages. Generally, adding more TPU to the LDPE/TPU blend gives rise to the amplification ratio. The pure LDPE flexure hinge has the lowest amplification ratio of 2.85, while the 25% TPU blend has the highest amplification ratio of 10.504. From 0 to 15%, increasing the TPU percentage leads to a strong improvement in the amplification ratio. Adding 15% TPU  
Figure 7: Average displacement diagrams of LDPE blend flexure hinge at different TPU percentages. results in the highest improvement rate compared to other cases. Specifically, from 15% to 25%, the amplification ratio only experiences a slight improvement from 9.376 to 10.504. The reason could be the good compatibility of the TPU with the LDPE polymer when adding 5-15%, as mentioned in the following figure. Adding more than 15% TPU leads to a lower efficiency as the LDPE/TPU blend is saturated. The average amplification ratio values of PP, ABS, and HDPE flexure hinges are 5.35, 7.60, and 5.02, respectively. Compared to the PP, ABS, and HDPE flexure hinge, the LDPE/TPU blend hinge has a wider range of amplification ratio of 2.85-10.504.