# Amplification Ratio of a Recycled Plastics-Compliant Mechanism Flexure Hinge
## 3 Results and Discussion  
### Amplification of PP, ABS, and HDPE Flexure Hinges  
This section examines the effects of the recycle ratio on the displacement of the PP, ABS, and HDPE flexure hinges. Firstly, we survey the impact of the recycle ratio on the displacement of the PP hinge. For each recycle ratio, we measured five samples. The average input and output parameters of PP hinges at different recycle ratios are presented in Table 2.  
Figure 3 shows the average displacement diagrams of the PP flexure hinge with various recycle ratios. With a maximum input value of 157 \(\upmu\)m, the average output value is 886 \(\upmu\)m, indicating the hinge's strong amplification rate. The regression equations between the average values of the input and output displacements are as follows:  
\[y_{1}=5.728x_{1} \tag{1}\]  
\[y_{2}=5.50x_{2} \tag{2}\]  
\[y_{3}=5.381x_{3} \tag{3}\]  
\[y_{4}=5.288x_{4} \tag{4}\]  
\[y_{5}=5.183x_{5} \tag{5}\]  
\[y_{6}=5.036x_{6} \tag{6}\] \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline Input (\(\upmu\)m) & 0 & 34 & 53 & 64.5 & 74 & 86 & 101.5 & 112.5 & 120 & 132 & 157 \\ \hline Output 25\% (\(\upmu\)m) & 0 & 98 & 202 & 294 & 357 & 425 & 504 & 572 & 627 & 691 & 814 \\ \hline Output 20\% (\(\upmu\)m) & 0 & 100 & 208 & 298 & 361 & 434 & 512 & 600 & 646 & 713 & 839 \\ \hline Output 15\% (\(\upmu\)m) & 0 & 109 & 212 & 301 & 364 & 438 & 527 & 615 & 660 & 726 & 856 \\ \hline Output 10\% (\(\upmu\)m) & 0 & 112 & 219 & 308 & 373 & 458 & 547 & 620 & 666 & 741 & 861 \\ \hline Output 5\% (\(\upmu\)m) & 0 & 121 & 228 & 312 & 384 & 487 & 558 & 626 & 681 & 764 & 867 \\ \hline Output 0\% (\(\upmu\)m) & 0 & 145 & 257 & 339 & 414 & 498 & 584 & 651 & 706 & 797 & 886 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average input and output parameters of PP hinges at different recycle ratios. Figure 2: The fixture and measurement device of the plastic flexure hinge: (**a**) fixture; and (**b**) measurement device setup. where \(y_{1}\), \(y_{2}\), \(y_{3}\), \(y_{4}\), \(y_{5}\), and \(y_{6}\) are the output data; and \(x_{1}\), \(x_{2}\), \(x_{3}\), \(x_{4}\), \(x_{5}\), and \(x_{6}\) are the input data of the PP flexure hinge at recycle ratios of 0%, 5%, 10%, 15%, 20%, and 25%, respectively. We created the regression equations using the trendline option in Excel software. The accuracy in these cases is calculated based on the R-square value of the trendline, which varies around 0.92-0.99. These are good enough as an R-square value of 0.9 is a good value with high accuracy. These equations show that the amplification ratio values are 5.728, 5.50, 5.381, 5.288, 5.183, and 5.03, which correspond to the PP flexure hinge at recycle ratios of 0%, 5%, 10%, 15%, 20%, and 25%. Generally, increasing the recycle ratio leads to a slight decline in the amplification ratio. The most significant result is that raising the input value typically results in a linear increase in the output value. At recycle ratio of 0%, the PP flexure hinge achieves the highest amplification ratio of 5.728. However, at a recycle ratio of 25%, the PP flexure hinge gains the lowest amplification ratio of 5.036, which is 12% lower than the highest one. The reason for this reduction is the degradation of the recycled PP component, leading to a weaker polymer as the recycle ratio increases. The amplification ratio of the PP hinge is primarily smaller when compared to the aluminum alloy flexure hinge, which has an amplification of 41 in [PERSON] et al. 's report [31]. The reasons are the higher strength and stiffness of the aluminum alloy and the 3D bridge-type of the aluminum alloy hinge compared to the 2D bridge type of PP plastic. The average input and output parameters for ABS hinges at various recycle ratios are shown in Table 3. The results from Table 3 are illustrated in Figure 4. With the maximum input value of 115 \(\upmu\)m, the average output value is 833 \(\upmu\)m, indicating the high amplification rate of the hinge.