# Amplification Ratio of a Recycled Plastics-Compliant Mechanism Flexure Hinge
## 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, [PERSON] 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. [PERSON] 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. [PERSON] 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, [PERSON] 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. [PERSON] 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 \(\upmu\)m 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.