# Amplification Ratio of a Recycled Plastics-Compliant Mechanism Flexure Hinge
## 3 Results and Discussion
### Amplification of PP, ABS, and HDPE Flexure Hinges
The regression equations between the average input and output displacement values are given as follows:  
\[y_{7} =8.249x_{7} \tag{7}\]  
\[y_{8} =7.843x_{8} \tag{8}\]  
\[y_{9} =7.646x_{9} \tag{9}\]  
\[y_{10} =7.506x_{10} \tag{10}\]  
Figure 3: Average displacement diagrams of PP flexure hinge at different recycle ratios. \[y_{11}=7.233x_{11} \tag{11}\]  
Figure 2:0  
where \(y_{7}\), \(y_{8}\), \(y_{9}\), \(y_{10}\), \(y_{11}\), and \(y_{12}\) are the output data; and \(x_{7}\), \(x_{8}\), \(x_{9}\), \(x_{10}\), \(x_{11}\), and \(x_{12}\) are the input data of the ABS flexure hinge at recycle ratios of 0%, 5%, 10%, 15%, 20%, and 25%. The amplification ratio values are 8.249, 7.843, 7.646, 7.506, 7.233, and 7.152, which correspond to the ABS flexure hinge at recycle ratios of 0%, 5%, 10%, 15%, 20%, and 25%. In general, raising the recycle ratio leads to a small reduction in the amplification ratio. Most notably, increasing the input value usually results in a linear increase in the output value. At a recycle ratio of 0%, the ABS flexure hinge achieves the highest amplification ratio of 8.249. However, at a recycle ratio of 25%, the ABS flexure hinge gains the lowest amplification ratio of 7.152, which is 13.3% lower than the highest one. This decrease is due to the degradation of the recycled ABS component, which results in a weaker polymer as the recycle ratio increases. Compared to the spring steel flexure hinge with an amplification of 13-15 reported by [PERSON] et al. (2016), the amplification ratio of the ABS hinge is mainly lower. The reasons are the higher strength and stiffness of the spring steel compared to the ABS plastic. Additionally, the ABS flexure hinge has a much higher amplification ratio than the PP one. Table 4 presents the average input and output parameters of HDPE hinges at different recycle ratios. The results from Table 4 are illustrated in Figure 2:1 Figure 5 presents the  
Figure 2:2 Displacement of the ABS flexure hinge at different recycle ratios. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline Input (\(\mathrm{\SIUnitSymbolMicro m}\)) & 0 & 15 & 27 & 34 & 41 & 45 & 55 & 63 & 70 & 85 & 115 \\ \hline Output 25\% (\(\mathrm{\SIUnitSymbolMicro m}\)) & 0 & 82 & 141 & 214 & 285 & 346 & 436 & 482 & 550 & 653 & 739 \\ \hline Output 20\% (\(\mathrm{\SIUnitSymbolMicro m}\)) & 0 & 85 & 164 & 207 & 281 & 344 & 435 & 482 & 568 & 661 & 748 \\ \hline Output 15\% (\(\mathrm{\SIUnitSymbolMicro m}\)) & 0 & 87 & 174 & 231 & 285 & 357 & 444 & 512 & 599 & 677 & 771 \\ \hline Output 10\% (\(\mathrm{\SIUnitSymbolMicro m}\)) & 0 & 96 & 181 & 238 & 286 & 363 & 457 & 531 & 624 & 684 & 773 \\ \hline Output 5\% (\(\mathrm{\SIUnitSymbolMicro m}\)) & 0 & 97 & 189 & 246 & 305 & 364 & 467 & 542 & 643 & 713 & 783 \\ \hline Output 0\% (\(\mathrm{\SIUnitSymbolMicro m}\)) & 0 & 108 & 204 & 260 & 324 & 399 & 489 & 560 & 666 & 741 & 833 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average input and output parameters of ABS hinges at different recycle ratios. average displacement diagrams of the different recycle ratios of the HDPE flexure hinge. With the maximum input value of 175 \(\upmu\)m, the average output value is 857 \(\upmu\)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:  
\[y_{13} =5.668x_{13} \tag{13}\] \[y_{14} =5.404x_{14}\] (14) \[y_{15} =5.159x_{15}\] (15) \[y_{16} =4.852x_{16}\] (16) \[y_{17} =4.616x_{17}\] (17) \[y_{18} =4.436x_{18} \tag{18}\]  
where \(y_{13}\), \(y_{14}\), \(y_{15}\), \(y_{16}\), \(y_{17}\), and \(y_{18}\) are the output data; and \(x_{13}\), \(x_{14}\), \(x_{15}\), \(x_{16}\), \(x_{17}\), and \(x_{18}\) are the input data of the HDPE flexure hinge at recycle ratios of 0%, 5%, 10%, 15%, 20%, and 25%.