Introduction

A mechanism that transmits forces and movements using elastic deformation is referred to as a Compliant Mechanism. Examples of this include springs and snap-fit features in plastic products.

At Nature Architects, we enhance functionality and reduce manufacturing costs by integrating products composed of multiple components using compliant mechanisms.

In this article, we will focus on the design of a "folding hanger" as a case study for utilizing compliant mechanisms. We will present the design approach and discuss specific design flow, including internal tools.

Design Challenge

To enhance portability and storage, many clothes hangers that can be folded are commercially available. Upon examining 10 products listed on an online shopping site, it was found that they generally require assembly of 3 to 10 components based on their images.

In this article, we will design a folding hanger using compliant mechanisms to meet the following objectives:

Design Concepts

• Create a monolithic folding hanger.
• Achieve compactness during molding (efficient use of mold surface area).

The design requirements for the folding hanger are as follows, based on average dimensions of commercially available products:

Design Requirements

• Shape suitable for hanging clothes when unfolded.
• Unfolded width: 400mm.
• Folded width: Below 100mm.
• Thickness (depth in the illustration): Below 15mm.
• Transition load from folding to unfolding state: 3N±10%.

Additionally, we consider the following manufacturing constraints:

Manufacturing Constraints

• Shape: Suitable for injection molding without undercuts.
• Material: POM M90-44 (Young's modulus 2500MPa, Poisson's ratio 0.35).
• Allowable stress: 31MPa (to achieve a creep life of 10 years).

Mechanism Selection

Commercially available folding hangers have various deformation mechanisms. Typically, they consist of rigid parts that do not deform and hinge parts that provide rotational freedom. To achieve integration, we need to replace the hinges with compliant mechanisms.

There are various types of hinge shapes used in compliant mechanisms, and the selection depends on the required degrees of freedom, reaction forces, and manufacturing constraints. Sometimes a combination of multiple mechanisms is used.

Created by modifying "Pin Flexure", "Blade Flexure", and "Notch Flexure" © 2017 OptoMechEngineer (Licensed under CC BY-SA 4.0)

In this case, due to the need for planar deformation and significant deformation, we select the Blade Flexure mechanism. While Notch Flexure, which provides only one rotational degree of freedom, would be more precise if purely replacing the hinge function, we prioritize large deformation within the allowable stress range. Hence, Blade Flexure is chosen.

Blade Flexure is often molded as a thin living hinge with a thickness of about 0.2mm to 0.4mm. However, for this folding hanger design, we require a force of approximately 3N to transition from the folded state to the unfolded state. To achieve this, we opt for a thicker and longer dimension to create a bow-like structure for practical use.

Overall Design

Below is an illustration of the hanger's structure, assembly, and opening/closing operation.

After molding the left side of the figure, assembling the "Hinge" creates the "Folded State." Subsequently, by manually manipulating the hinge or the straight section, the hanger can be folded and unfolded.

The "Hinge" functions as a hinge when assembled after demolding. While it could be designed as an integrated living hinge, we opted for an assembly-type hinge due to the difficulty of molding in the front-to-back direction and concerns about durability.

The "Bow Section" can be seen as a combination of multiple Blade Flexures. As a standalone mechanism, it has weakened constraints on the degrees of freedom due to its curved connections and significant deformation. In this design, we prioritize the deformation amount, reaction force, and the shape of the hanger when expanded.

The "Straight Section" plays a role in maintaining a constant distance between the hinge and the bottom end of the bow section. To function as a nearly rigid part, it requires sufficient bending rigidity.

Custom Design Environment

How can we design a curved beam that takes on the shape of a hanger after deformation? It is relatively straightforward when the movement is simple or when we can assume small deformations. However, in this case, the beam undergoes significant deformation over a broad range, requiring numerous iterations of shape modifications and analysis result verifications. It becomes challenging to achieve this using the conventional CAD + CAE environment.

At our company, we have independently developed various design environments that operate on the 3D CAD software Rhinoceros through a plug-in called Grasshopper. We can flexibly switch between these environments based on the design problem. (More about Grasshopper can be found in a previous article.)

For this project, we will use an environment where we can model the beam with 2D beam elements and observe deformations in real-time. By utilizing this environment, we can efficiently explore numerous shapes and discover mechanisms that achieve the desired deformations.

Shape Considerations

Using the aforementioned tool, we will proceed to realize the shapes of the bow section and straight section.

After configuring the analysis settings and modeling the shapes during molding, we can immediately run the analysis. This allows us to confirm:

• Shapes in the folded and unfolded states.
• Forces required for deformation.
• Maximum stresses during intermediate stages.

The boundary conditions are set such that the root of the hook section is fixed, the hinge is initially displaced in the X-direction to create the assembly state, and then displaced in the Y-direction to reach the unfolded state.

As a result of exploring while confirming the above three items, we have identified the shape shown in the figure below that meets the requirements. The shape in the unfolded state is well-suited for a hanger.

The cross-sectional shape of the bow section is adjusted to be a thin rectangle in the bending direction to enhance the bending rigidity. For the final design (to be described in Part 2), we opted for the T-shape shown in the figure below.

The stresses and fixed part reaction forces during each deformation stage in the analysis are as follows (the values satisfy the initial requirements of 3N±10% and 31MPa or lower, respectively):

Detailed Design

With the shapes and cross-sections of the straight section and the bow section have been determined, we proceed to the detailed design. Considering the lock function for the hinge, the claw for creep prevention, cutouts in the hook section, and draft angles, we have finalized the shape as shown below. The shape is designed without undercuts for ease of manufacturing. Detailed information regarding the cutout in the hook section will be provided in Part 2.

As shown in the cross-sectional diagram below, the hinge section features a mechanism where the axis slides during unfolding and the rotation is locked.

Performance Confirmation through Detailed Analysis

Next, based on the 3D data from the detailed design, we perform structural analysis using general-purpose CAE software with solid elements to confirm the stress and reaction forces. The boundary conditions are set such that the root of the hook section is fixed, and the axis and hole of the hinge are displaced to replicate the deformation process: molding state ⇨ folding state ⇨ unfolding state.

The analysis results match the simulation in Grasshopper, confirming that the hanger takes on its shape when unfolded, and the reaction force is approximately 3N. The maximum stress from the solid element analysis is 32.5MPa (red solid line in the graph), which differs from the 24.2MPa stress obtained in the Grasshopper simulation. This discrepancy is likely due to the fact that the former represents the maximum stress in the beam elements and does not reflect stress concentrations in regions with small radii and draft angles.

As mentioned above, stress analysis in the linear material model exceeds the initial allowable stress of 31MPa. However, at this stress level, the effects of material nonlinearity are not negligible. The results of the nonlinear analysis indicate that the maximum stress is 22.8MPa (red dashed line in the graph), which is within the allowable stress range, making it acceptable.

When conducting design assessments using simplified models, it is crucial to secure a margin for the target value depending on the fidelity of the analysis model. In this case, the increase in stress due to accurate shape representation and the decrease in stress due to accurate material modeling counterbalance each other, resulting in the observed difference.

Prototype

Finally, we prototyped using a 3D printer to confirm that the mechanism functions as intended. Please refer to the video at the beginning.

Please note that we printed in PLA instead of POM, so the counterforce when transitioning states is lower than the design value.

Conclusion

In this article, we introduced the design of a folding hanger using compliant mechanisms as a case study of integrating multiple components. We hope this article has provided insights into the design approach and the possibilities of compliant mechanisms.

In the next part, we will provide a more detailed explanation of manufacturability.