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Article

Amplification Ratio of a Recycled Plastics-Compliant Mechanism Flexure Hinge

by
Tran Minh The Uyen
1,
Pham Son Minh
1,
Van-Thuc Nguyen
1,
Thanh Trung Do
1,
Hai Nguyen Le Dang
1 and
Van Thanh Tien Nguyen
2,*
1
Faculty of Mechanical Engineering, Ho Chi Minh City University of Technology and Education, Ho Chi Minh City 71307, Vietnam
2
Faculty of Mechanical Engineering, Industrial University of Ho Chi Minh City, Nguyen Van Bao Street, Ward 4, Go Vap District, Ho Chi Minh City 70000, Vietnam
*
Author to whom correspondence should be addressed.
Appl. Sci. 2023, 13(23), 12825; https://doi.org/10.3390/app132312825
Submission received: 4 November 2023 / Revised: 22 November 2023 / Accepted: 24 November 2023 / Published: 29 November 2023
(This article belongs to the Special Issue Advances in Plastic Production, Treatment and Recycling for Circular Economy)
Browse Figures
Versions Notes

Abstract

:
This research focuses on the fabrication of plastic flexure hinges from diverse plastics such as ABS, PP, HDPE, and LDPE. To enhance hinge efficiency, the recycling ratios are also investigated. The amplification ratio of different recycle ratios and plastic types are measured. The results show that the input and output displacements of all PP, ABS, and HDPE hinges are linear. The presence of recycled plastics has no impact on this basis. The pure PP, ABS, and HDPE flexure hinges achieve the highest amplification ratios of 5.728, 8.249, and 5.668. The addition of recycled plastics reduces the amplification ratio. This decrease in the amplification ratio, however, is small. At a 25% recycle ratio, the PP, ABS, and HDPE flexure hinges have 12%, 13.3%, and 21.7% lower amplification ratios than the pure plastic hinges. Furthermore, the utilization of recycled plastics may lessen the need for new plastic made from raw materials. With the PP flexure hinge, a maximum input value of 157 µm could result in an output value of 886 µm. At a maximum input value of 115 µm, the ABS flexure hinge could achieve an output value of 833 µm. Finally, a maximum input value of 175 µm might result in an output value of 857 µm when using the HDPE flexure hinge. The average amplification ratio values for all recycling ratios for PP, ABS, and HDPE flexure hinges are, respectively, 5.35, 7.60, and 5.02. The ABS flexure hinge frequently outperforms the PP and HDPE flexure hinge in terms of amplification ratios. Among these plastics, HDPE flexure hinges have the lowest amplification ratio. In general, increasing the thermoplastic polyurethane (TPU) content of the LDPE/TPU blend increases the amplification ratio. The cause could be the TPU’s high compatibility with the LDPE polymer. The LDPE/TPU blend hinge offers a broader range of the amplification ratio of 2.85–10.504 than the PP, ABS, and HDPE flexure hinges. It is interesting that changing the blend percentage has a much greater impact on the amplification ratio than changing the recycling ratio. The findings broaden the range of applications for plastic flexure hinges by identifying optimal plastic types. The impact of the hinge shape on the performance of the injected plastic flexure hinge might be studied in further research.

1. Introduction

A compliant mechanism is a flexible structure body that could transfer force, momentum, and movement based on the elastic deformation of the body [1,2,3]. The compliant mechanism is widely applied in robotics, precision devices, aerospace, and consumer products due to the advantages of no friction force and backlash [4,5,6]. During the loading process, the compliant mechanism structure is deformed, therefore, storing the elastic energy. After that, the energy in the compliant mechanism structure is released to perform its purpose [7,8,9]. There are many structural types of compliant mechanism structures such as beam flexures, shell flexures, sheet flexures, and combination structures [10,11,12,13].
A compliant mechanism structure can be used as a compliant flexure hinge for amplifier application in precision engineering. There are many types of compliant flexure hinges for amplifiers, for instance, elliptical type, notch type, circular type, and bridge type [14,15,16,17]. A bridge-type-compliant flexure hinge possesses the merits of a high ratio of the output displacement to the input displacement, a simple structure, and can suffer a high load. To design compliant flexure hinges, besides considering the hinge geometry, materials selection and manufacturability are also critical factors. For example, a compliant flexure hinge generated from conventional metallic materials is reliable but demands a complex process of manufacturing. A metallic flexure hinge is usually created by an electrical discharge machine (EDM), a wire-cutting machine, a 3D printing machine, or a laser cutting machine [18,19,20,21]. For example, Liu et al. [22] generated a triple-cross-spring flexure pivot in a wire-cutting machine. This flexure pivot achieves a large motion stroke and high precision; however, the assembly process could lead to a remarkable error. Wang et al. [23] rapidly produced a flexure hinge using a 3D printing machine combined with a wire cutting machine. Initially, the body of the flexure hinge is printed by a selective laser melting 3D printer. Thereafter, the body is machined via a precision wire-cutting machine. Coemert et al. [24] created titanium-based flexure hinges by laser cutting. The findings showed that the payload value is inversely proportional to the hinge length but proportional to hinge width.
The metallic flexure hinges often require a lot of time and cost to be created due to the complex structure and the high precision demand. Plastic-compliant flexure hinges appear to be an ideal alternative as this material is cheaper and can be more easily produced. For instance, Mutlu et al. [25] produced a 3D-printed flexure hinge using the thermoplastic elastomer (TPE) and discovered that the optimal designs are elliptic and non-symmetric. Specifically, plastic-compliant flexure hinges could be injected by an injection molding machine with high productivity. Rosa et al. [26] used the mesoscale injection molding to produce a flexure-based nanopositioner made from cyclic olefin copolymer (COC). The COC nanopositioner has a travel range of 15 µm and a maximum standard deviation of 52.3 nm. Remarkably, the recycled capacity of the plastics created a cheap substitute for metallic flexure hinges. Despite its advantages, injected plastic flexural hinge investigations are not widely used and require additional research. Recently, recycled plastics have been widely applied in many industrial fields. Even for the automotive industry, which usually requires high-quality materials, using recycled plastics is a good choice [27]. Automotive companies tend to increase the recycled plastics in their product [28,29]. Popular plastics such as ABS, PP, HDPE, and LDPE in the automotive industry have received much attention due to their high efficiency [30].
This investigation focuses on examining the injection plastic flexure hinge from the different types of polymers, including the ABS, PP, HDPE, and LDPE/TPU blend. The effect of the incorporated recycled polymer ratio was also investigated in order to maximize the hinge performance. The rates of amplification are measured and compared. The findings add to our understanding of plastic flexure hinges and widen their uses by identifying the best plastic kinds and recycle ratios.

2. Materials and Methods

2.1. Materials

The PP polymer named Advanced-PP 1100 N is supplied by the Advanced Petrochemical Company, Saudi Arabia. The ABS 750 SW polymer is manufactured by Kumho Petrochemical, Korea, while the HDPE polymer HTA 108 is imported by the Exxon Mobile Petroleum and Chemical Company, Saudi Arabia. The TPU polymer (TPU® TU90AE) is produced by Dongguan Rayan Polymer in China. LDPE polymer InnoPlus LD2426H is supplied from PPT company, Thailand. Besides examining the effects of plastic types, this study also surveys the impact of the recycled plastics ratio on the displacement rate. The recycle ratio of PP, ABS, and HDPE polymers ranges from 0% to 25%. Table 1 shows the injection mold parameters of the PP, ABS, and HDPE hinges. The ABS polymer blended with 0–25% TPU is also considered. The injection parameters in these tables are chosen based on the polymer properties, hinge shape, and injection molding equipment to ensure that they are receiving a good, injected sample. The filling speed and packing speed are expressed as a percentage of the injection machine’s injection rate, which is 154 g/s. The injection molding machine type used in this study is MA 1200III, Haitian, China. The average UTS values of PP, ABS, HDPE, LDPE, and TPU are 35 MPa, 48.5 MPa, 60 MPa, 11 MPa, and 55 MPa.

2.2. Methods

The flexure hinge design, compliant mechanism, and the injected hinge are shown in Figure 1. Figure 2 shows the fixture for the hinge, and the measurement tool with chronographs for determining the hinge’s displacement. The measurement process has three steps. Step 1: Attach the sample to the bracket in the correct position and attach the chronographs to the correct position. Step 2: Place the pusher in the middle of the measurement model so that it matches the measurement model and adjusts. All chronographs are set to zero. Step 3: Turn the handle on the pusher, and then observe the chronographs and record the results. These samples are injected with the sample mold; therefore, the thickness and geometries are the same. The testing process is conducted at 25 °C.

3. Results and Discussion

3.1. 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 µm, the average output value is 886 µm, indicating the hinge’s strong amplification rate. The regression equations between the average values of the input and output displacements are as follows:
y1 = 5.728x1
y2 = 5.50x2
y3 = 5.381x3
y4 = 5.288x4
y5 = 5.183x5
y6 = 5.036x6
where y1, y2, y3, y4, y5, and y6 are the output data; and x1, x2, x3, x4, x5, and x6 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 Chen 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 µm, the average output value is 833 µm, indicating the high amplification rate of the hinge. The regression equations between the average input and output displacement values are given as follows:
y7 = 8.249x7
y8 = 7.843x8
y9 = 7.646x9
y10 = 7.506x10
y11 = 7.233x11
y12 = 7.152x12
where y7, y8, y9, y10, y11, and y12 are the output data; and x7, x8, x9, x10, x11, and x12 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 Ling et al. [32], 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 5. Figure 5 presents the average displacement diagrams of the different recycle ratios of the HDPE flexure hinge. With the maximum input value of 175 µm, the average output value is 857 µm, indicating the high amplification rate of the hinge. The regression equations for the average values of the input and output displacements are as follows:
y13 = 5.668x13
y14 = 5.404x14
y15 = 5.159x15
y16 = 4.852x16
y17 = 4.616x17
y18 = 4.436x18
where y13, y14, y15, y16, y17, and y18 are the output data; and x13, x14, x15, x16, x17, and x18 are the input data of the HDPE flexure hinge at recycle ratios of 0%, 5%, 10%, 15%, 20%, and 25%.
The amplification ratio values are 5.668, 5.404, 5.159, 4.852, 4.616, and 4.436, which correspond to the HDPE flexure hinge at recycle ratios of 0%, 5%, 10%, 15%, 20%, and 25%. Generally, increasing the recycle ratio leads to a slight improvement in the amplification rate, which is similar to the PP and ABS cases. Most importantly, improving the input value mostly leads to a linear increase in the output value. At a recycle ratio of 0%, the HDPE flexure hinge has the highest amplification ratio of 5.668. At a recycle ratio of 25%, the HDPE flexure hinge achieves the lowest amplification ratio of 4.436, which is 21.7% lower than the highest. The amplification ratio of the HDPE hinge is primarily lower when compared to the titanium alloy flexure hinge with an amplification of 6.0 in Fiaz et al.’s work [33]. The reason for this is that titanium alloys have a higher strength and rigidity than the HDPE plastic. Additionally, the HDPE flexure hinge’s amplification ratio is significantly lower than that of the ABS flexure hinge.
Overall, all the PP, ABS, and HDPE hinges have linear relationships between the input and output displacement. This principle is unchanged by the presence of recycled plastics. Additionally, adding recycled plastics causes the amplification ratio to decrease. This decrease in the amplification ratio, however, is small. At a 25% recycle ratio, the PP, ABS, and HDPE flexure hinges gain an amplification ratio that is 12%, 13.3, and 21.7% lower than the pure plastic hinges. Additionally, using recycled plastics could reduce the need for new plastic made from raw materials.

3.2. Comparison between PP, ABS, and HDPE Flexure Hinges

In this section, the displacements of the HDPE are compared with the previous results of the ABS and PP flexure hinges. The input and output equations at different recycle ratios are presented in Table 5. Figure 6 shows a more visual representation of these results.
Figure 6 shows the comparison of the amplification ratio among the PP, ABS, and HDPE flexure hinges at different recycle ratios. The pure PP, ABS, and HDPE flexure hinges achieve the highest amplification ratios of 5.728, 8.249, and 5.668. The average amplification ratio values of all recycle ratios are 5.35, 7.60, and 5.02 corresponding to the PP, ABS, and HDPE flexure hinges. Generally, the ABS flexure hinge has the highest amplification ratios, followed by the PP flexure hinge. HDPE flexure hinge has the lowest highest amplification ratios among these plastic types. The reason is for this is the order’s gradual reduction in the tensile strength and elastic modulus of the PP, ABS, and HDPE plastics. Moreover, the highest amplification ratio is 8.249, gained by the ABS flexure hinge in the packing pressure case. In reverse, the HDPE flexure hinge in the cooling time case has the lowest amplification ratio of 4.436.
Table 6 presents the amplification ratios of some common flexure hinge materials to compare the amplification ratio of these plastic hinges with other materials. The aluminum alloys and spring steel could produce a flexure hinge with a greater amplification ratio compared to the PP, ABS, and HDPE flexure hinges due to the stronger mechanical properties [31,32]. The amplification ratios of the PP, ABS, and HDPE flexure hinges are compatible with smart memory alloys and titanium alloys [33,34].
In general, the HDPE flexure hinge has the lowest amplification ratio compared to the ABS and PP flexure hinges. It is interesting to note that these plastic hinges have amplification ratios that could be like those of titanium alloy hinges but lower than those of the spring steel and aluminum alloy hinges. More research could explore the effects of the hinge shape on the performance of the injected plastic flexure hinge.

3.3. 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% 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 µm, the average output value is 947 µm, indicating the high amplification rate of the hinge. The regression equations for the average values of the input and output displacements are as follows:
y19 = 2.853x19
y20 = 4.517x20
y21 = 6.323x21
y22 = 9.376x22
y23 = 10.37x23
y24 = 10.504x24
where y19, y20, y21, y22, y23, and y24 are the output data; and x19, x20, x21, x22, x23, and x24 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 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. Notably, modifying the blend percentage causes a greatly higher change rate in the amplification ratio than changing the recycle ratio. This result is consistent with the study by Thomas et al. [35], which indicated that if the TPU percentage is less than 80%, blending TPU into LDPE could result in a better tensile strength due to the good compatibility between them. The improvement in the tensile strength could lead to a better amplification ratio of the LDPE/TPU blend.
Figure 8 shows the SEM microstructure of different plastic flexure hinges. Figure 8a–c shows a smooth surface, indicating the homogeneous structure of ABS, PP, and HDPE plastics. Notably, Figure 8d shows a heterogeneous microstructure, with some particles presenting the TPU phase in the LDPE matrix, pointing out the good compatibility of the TPU with the LDPE polymer. The presence of the TPU phase helps improve the mechanical properties of the LDPE/TPU blends, leading to a higher amplification ratio.

4. Conclusions

This study focuses on making plastic flexure hinges out of various plastics such as ABS, PP, HDPE, and LDPE/TPU blend. The recycle ratios are also examined to improve the hinge efficiency. The amplification ratios of different recycle ratios and plastic types were measured and compared. Some interesting results that could be named are:
  • The input and output displacements of all PP, ABS, and HDPE hinges are in a linear relationship. The existence of recycled plastics has no effect on this principle. The pure PP, ABS, and HDPE flexure hinges achieve the highest amplification ratios of 5.728, 8.249, and 5.668. The amplification ratio is lowered by the addition of recycled plastics. However, this amplification ratio reduction is not very high. In comparison to pure plastic hinges, the 25% recycling ratio PP, ABS, and HDPE flexure hinges obtain an amplification ratio that is 12%, 13.3, and 21.7% lower. Furthermore, the use of recycled plastics could reduce the requirement for new plastic created from raw resources.
  • With the PP flexure hinge, a maximum input value of 157 µm could lead to an output value of 886 µm. However, the ABS flexure hinge could gain an output value of 833 µm at a maximum input value of 115 µm. Finally, with the HDPE flexure hinge, a maximum input value of 175 µm could lead to an output value of 857 µm. For the PP, ABS, and HDPE flexure hinges, respectively, the average amplification ratio values of all recycling ratios are 5.35, 7.60, and 5.02. In terms of amplification ratios, the ABS flexure hinge is often better than the PP and HDPE flexure hinge. The HDPE flexure hinges have the lowest amplification ratio among these plastic types.
  • The amplification ratio typically develops as more TPU is added to the LDPE/TPU blend. The TPU’s strong compatibility with the LDPE polymer may be the reason for this. The LDPE/TPU blend hinge offers a broader range of amplification ratio of 2.85–10.504 than the PP, ABS, and HDPE flexure hinges. It is noteworthy that altering the blend percentage has a much greater impact on the amplification ratio than adjusting the recycling ratio. By identifying the best plastic kinds, the findings expand the range of uses for plastic flexure hinges. Besides finding suitable plastics, further investigations could survey the effects of the hinge shape, the hinge dimension, and the hinge design on its performance. The temperature condition, humidity, and degradation could also impact the plastic flexural hinge and need further investigation.

Author Contributions

P.S.M. and V.-T.N.: conceptualization, funding acquisition; V.-T.N.: writing original draft, investigation; T.M.T.U., T.T.D., P.S.M., H.N.L.D. and V.-T.N.: analyzing, visualization, project administration; V.T.T.N., H.N.L.D., P.S.M. and V.-T.N.: writing—review and editing. All authors have read and agreed to the published version of the manuscript.

Funding

The authors acknowledge the support of HCMC University of Technology and Education for this study.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data is contained within the article.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Plastic bridge—type flexure hinge: (a) 2D design; (b) compliant mechanism of the hinge; and (c) injection molding hinge.
Figure 1. Plastic bridge—type flexure hinge: (a) 2D design; (b) compliant mechanism of the hinge; and (c) injection molding hinge.
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Figure 2. The fixture and measurement device of the plastic flexure hinge: (a) fixture; and (b) measurement device setup.
Figure 2. The fixture and measurement device of the plastic flexure hinge: (a) fixture; and (b) measurement device setup.
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Figure 3. Average displacement diagrams of PP flexure hinge at different recycle ratios.
Figure 3. Average displacement diagrams of PP flexure hinge at different recycle ratios.
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Figure 4. Displacement of the ABS flexure hinge at different recycle ratios.
Figure 4. Displacement of the ABS flexure hinge at different recycle ratios.
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Figure 5. Displacement of HDPE flexure hinges at different recycle ratios.
Figure 5. Displacement of HDPE flexure hinges at different recycle ratios.
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Figure 6. Comparison between the displacement ratios between the PP, ABS, and HDPE flexure hinges at different recycle ratios.
Figure 6. Comparison between the displacement ratios between the PP, ABS, and HDPE flexure hinges at different recycle ratios.
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Figure 7. Average displacement diagrams of LDPE blend flexure hinge at different TPU percentages.
Figure 7. Average displacement diagrams of LDPE blend flexure hinge at different TPU percentages.
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Figure 8. SEM microstructure of the plastic flexure hinges: (a) ABS, (b) PP, (c) HDPE, and (d) LDPE/TPU.
Figure 8. SEM microstructure of the plastic flexure hinges: (a) ABS, (b) PP, (c) HDPE, and (d) LDPE/TPU.
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Table 1. Injection the molding parameters of PP, ABS, HDPE, and LDPE/TPU flexure hinges.
Table 1. Injection the molding parameters of PP, ABS, HDPE, and LDPE/TPU flexure hinges.
ParametersPP ABSHDPELDPE/TPU
Filling pressure (bar)40432625
Filling speed (%)75756560
Filling time (s)2222
Packing pressure (bar)45382320
Packing speed (bar)75706060
Packing time (s)2111
Temperature (°C)200210205200
Table 2. Average input and output parameters of PP hinges at different recycle ratios.
Table 2. Average input and output parameters of PP hinges at different recycle ratios.
Input (μm)0345364.57486101.5112.5120132157
Output 25% (μm)098202294357425504572627691814
Output 20% (μm)0100208298361434512600646713839
Output 15% (μm)0109212301364438527615660726856
Output 10% (μm)0112219308373458547620666741861
Output 5% (μm)0121228312384487558626681764867
Output 0% (μm)0145257339414498584651706797886
Table 3. Average input and output parameters of ABS hinges at different recycle ratios.
Table 3. Average input and output parameters of ABS hinges at different recycle ratios.
Input (μm)0152734414555637085115
Output 25% (μm)082141214285346436482550653739
Output 20% (μm)085164207281344435482568661748
Output 15% (μm)087174231285357444512599677771
Output 10% (μm)096181238286363457531624684773
Output 5% (μm)097189246305364467542643713783
Output 0% (μm)0108204260324399489560666741833
Table 4. Average input and output parameters of HDPE hinges at different recycle ratios.
Table 4. Average input and output parameters of HDPE hinges at different recycle ratios.
Input (μm)015254050638095113138175
Output 25% (μm)089157228283341413458493524745
Output 20% (μm)0102160245294360424461507576762
Output 15% (μm)0105166254309360445502544615785
Output 10% (μm)0110172264319374474548611684790
Output 5% (μm)0107178274336415493584646715814
Output 0% (μm)0115194290353450532608662744857
Table 5. Displacement equations of the PP, ABS, and HDPE plastics flexure hinge at different recycle ratios.
Table 5. Displacement equations of the PP, ABS, and HDPE plastics flexure hinge at different recycle ratios.
Recycle RatioPPABSHDPE
25%y1 = 5.728x1y7 = 8.249x7y13 = 5.668x13
20%y2 = 5.50x2y8 = 7.843x8y14= 5.404x14
15%y3 = 5.381x3y9 = 7.646x9y15 = 5.159x15
10%y4 = 5.288x4y10 = 7.506x10y16 = 4.852x16
5%y5 = 5.183x5y11 = 7.233x11y17 = 4.616x17
0%y6 = 5.036x6y12 = 7.152x12y18 = 4.436x18
Average ratio5.357.605.02
Table 6. Amplification ratios of different flexure hinge materials.
Table 6. Amplification ratios of different flexure hinge materials.
MaterialsAmplification RatioReferences
PP5.35This report
ABS7.6This report
HDPE5.02This report
Aluminum alloys41Chen et al. [31]
Spring steel13–15Ling et al. [32]
Titanium alloys6.0Fiaz et al. [33]
Smart memory alloys2.2Maffiodo et al. [34]
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MDPI and ACS Style

Uyen, T.M.T.; Minh, P.S.; Nguyen, V.-T.; Do, T.T.; Nguyen Le Dang, H.; Nguyen, V.T.T. Amplification Ratio of a Recycled Plastics-Compliant Mechanism Flexure Hinge. Appl. Sci. 2023, 13, 12825. https://doi.org/10.3390/app132312825

AMA Style

Uyen TMT, Minh PS, Nguyen V-T, Do TT, Nguyen Le Dang H, Nguyen VTT. Amplification Ratio of a Recycled Plastics-Compliant Mechanism Flexure Hinge. Applied Sciences. 2023; 13(23):12825. https://doi.org/10.3390/app132312825

Chicago/Turabian Style

Uyen, Tran Minh The, Pham Son Minh, Van-Thuc Nguyen, Thanh Trung Do, Hai Nguyen Le Dang, and Van Thanh Tien Nguyen. 2023. "Amplification Ratio of a Recycled Plastics-Compliant Mechanism Flexure Hinge" Applied Sciences 13, no. 23: 12825. https://doi.org/10.3390/app132312825

APA Style

Uyen, T. M. T., Minh, P. S., Nguyen, V. -T., Do, T. T., Nguyen Le Dang, H., & Nguyen, V. T. T. (2023). Amplification Ratio of a Recycled Plastics-Compliant Mechanism Flexure Hinge. Applied Sciences, 13(23), 12825. https://doi.org/10.3390/app132312825

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