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Origami 2.3

A national flag measuring 600 square meters was prepared using 2.3 lakh origami boats, which set a record. The work was completed in seven hours on the campus of the Academy situated by the Bengaluru-Hosur national highway, said sources.

Origami 2.3

In addition, future designs will be lighter, which will allow for larger models, and the arms will be strong enough to survive crashes. The same origami principles could be generalized to any type of flying vehicle with wings or with protective cages, the researchers said.

In many origami-based applications, a device needs to be maintained in one or more fold states. The origami stability integration method (OSIM) presented in this paper provides an approach for graphically combining various techniques to achieve stability. Existing stability techniques are also categorized into four groups based on whether they are intrinsic or extrinsic to the origami pattern and whether they exhibit gradual or non-gradual energy storage behaviors. These categorizations can help designers select appropriate techniques for their application. The paper also contains design considerations and resources for achieving stability. Finally, two case studies are presented which use the OSIM and the technique categorization to conceptualize stability in origami-based devices.

However, the ability of origami-based devices to fold can also make them mechanically unstable and lead to undesired motion or behaviors. The balance between retaining foldability and providing adequate stability is a fundamental challenge for origami-based design. While many techniques exist for creating stability in origami-based devices, major difficulties for designers lie in (1) determining which techniques to use and (2) how they will interact with the chosen origami pattern, the loading conditions, and other techniques.

This paper addresses these difficulties by presenting a method for classifying origami stability and by introducing the origami stability integration method (OSIM), a design tool for visualizing and predicting how stability can be achieved in origami devices with the combination of techniques and loading conditions. The paper is outlined as follows: review of background material (Sec. 2), description of the OSIM (Sec. 3), discussion on stability technique categorization (Sec. 4), description of select stability techniques (Sec. 5), and presentation of two case studies (Sec. 6).

The motion of origami can be modeled as a kinematic linkage [8,13,14]; the facets are modeled as links, the creases as hinge joints, and origami vertices as spherical mechanisms [15], as shown in Fig. 1. Thinking of origami as a kinematic linkage allows designers to apply engineering concepts (such as mechanical advantage [16], motion prediction [17], and stability [18]) to origami design.

Other techniques not incorporated as part of the creases or facets include clasps, magnets, actuators, and other constraints [37,38]. For example, the origami solar array [12] uses an expanding external frame (fitted with torsional springs) to pull the array into the unfolded fold state, as shown in Fig. 3.

An expanding external frame (shown in white) is the stability technique used to pull open the origami solar array [12], creating a stable unfolded fold state. This image shows the array mid-deployment.

The OSIM is a design tool for visualizing and planning stable equilibria in origami-based devices. This section addresses preliminary concepts, describes the steps of the OSIM, and provides an example.

To facilitate the discussion of origami in the OSIM, two concepts, origami linkage and fold-state continuum, are introduced. The term origami linkage provides a way to discuss the facets and creases of a fold state without referring to the fold angles. The fold-state continuum provides a simple way to represent a range of fold states.

Most origami-based devices utilize the movement of multiple vertices. However, the common terms used to discuss origami as a kinematic linkage (such as origami vertex, origami figure, configuration, fold state, and crease pattern) either do not refer to a generalized set of facets and creases or they imply a static position. To address these limitations, a new term, origami linkage, is presented.

An origami linkage is a set of planar facets and their interconnecting creases. This term builds on the traditional use of the term linkage in engineering to emphasize that the members exist independent of their position and to strengthen the concept that origami can be an engineering tool. The term origami linkage will be used in the OSIM because the set of facets and creases is represented for a range of its fold angles (not just one fold state).

An origami linkage can be as simple as a single vertex or multiple vertices, as shown in Fig. 4. Typically, an origami linkage has an equivalent spherical mechanism. A fold state is an origami linkage in a defined position.

As an origami linkage folds, it progresses through a continuous set of fold states that can form a continuum. A fold-state continuum is a useful tool in analyzing and understanding the range of motion of an origami linkage and the properties of the linkage throughout the folding process.

The fold-state continuum for a single DOF origami linkage can be plotted along a single line, as seen in Fig. 5. This 1D continuum is used as the x-axis in the OSIM. Linkages with multiple DOF can also be represented using a 1D fold-state continuum using symmetry or other constraints (such as constraints applied by a user during manipulation) [21,22,45]. Care should be taken to ensure that origami linkages deploy correctly from any change-point position (such as the fully unfolded state).

A 1D fold-state continuum of a single DOF origami linkage in Fig. 4. Seven fold states along the continuum are shown and marked on the continuum (three are labeled). Dashed arrows are also included on some fold states to help visualize the position.

Joints in spherical mechanisms can undergo continuous rotation. However, origami linkages typically interfere at 180 deg due to adjacent facet interference. Other constraints, such as limited facet extension, may further limit the motion. Because of this, 1D fold-state continuums are usually limited to a certain range bounded by the possible motion of the origami linkage. This is represented as vertical lines on either side of the continuum, as shown in Fig. 5.

Designate zones critical to the function of the origami-based device, as shown in Fig. 6. Desired stability zones: Stable fold states are desired in the final device. Ideally, origami linkages are stable in a single, predetermined fold state (i.e., one position along the continuum). However, some margin of error is often acceptable. The width of the desired stability zone corresponds with this acceptable stability tolerance.

Different combinations of techniques and linkages can produce favorable results. As such, the steps of the OSIM are meant to be an iterative process. Throughout the process, the origami linkage could be modified or replaced. A well-designed origami linkage and loading conditions can reduce the number of techniques necessary for achieving the desired energy conditions. For example, while most loading conditions create instability in the unfolded state, the linkage used for the origami colander [46] (shown in Fig. 7)1 effectively uses the loading condition to bias toward a stable equilibrium. Gravity pulls the side facets into extension and this creates stability.

An origami-based colander that uses the limited facet extension technique in combination with the loading condition (gravity) to achieve stability in its unfolded state (image used with permission from B&R Plastics, Inc)

The PUJ tub is an origami-based product that is flat for storage and can be folded into a seat shape and placed in a sink to be used as a baby bathtub.2 While the OSIM was not used to design stability in this product, it is used here to illustrate the steps of the OSIM (see Fig. 8). Step 1: A 2-DOF origami linkage is selected. This origami linkage is not rigidly foldable, so a flexible foam is used.

An intrinsic stability technique assists in realizing stable equilibria using only the creases and facets of an origami linkage. Examples include hinge interference, compliant joints, and non-rigidly foldable linkages [5]. In this paper, stimuli-actuated techniques are also considered intrinsic despite the need for outside influence.

Benefits: The primary advantage of intrinsic techniques is that they only involve the members of the origami linkage, meaning they do not require additional parts. For applications that are concerned with appearance, these techniques can highlight the simple, elegant nature of origami.

Drawbacks: Intrinsic techniques achieve stability using the geometry and material of the origami linkage. This creates two disadvantages. First, these techniques are limited by the material of the origami linkage. For example, if the device must be made from a stiff or brittle material, it could be difficult to create good torsional springs for large deflection. However, advances in materials and methods for increasing material compliance are making intrinsic techniques more accessible.

Another challenge is that these techniques usually place constraints on which origami linkages can be used because the two affect each other. For example, if the facet interference technique is selected to help maintain a non-planar fold state, the origami linkage must either be non-flat foldable or have more than one degree-of-freedom [47,48]. 041b061a72

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