Material selection There are several design options for the general material of an origami-adapted product

Material selection
There are several design options for the general material of an origami-adapted product;
these depend on whether the material needs to be flexible, rigid, a hybrid of the two or have multiple flexible layers. Origami is primarily constructed out of paper which is a flexible material that allows flexing in the panels while folding. Special considerations must be made in order to do origami with a rigid material, hence it is ideal to research and decide the material and design options early on in product development since it affects the remainder of the design.
Two considerations in selecting the general material are the rigidity and continuity requirements of the product. Rigidity refers to the stiffness of the material and has no allowance for deformation in the panels. Continuity refers to a closed surface without any perforations or interruptions. These two design considerations combine to result in four different general material design options.
The four general material design options are rigid, flexible, multiple flexible layers and
hybrid. Figure 2.7 shows how these two considerations influence the general material selection.
For products that need to be rigid and continuous this results in a hybrid material. A hybrid
material has rigid panels with a flexible membrane. If a rigid material needs to be cut to allow folding, continuity is maintained with the adhesion of a flexible membrane or a flexible material solely at the creases. For products that need to be rigid and interrupted (non-continuous) this results a rigid material that can have cuts or slits. Products that need to be flexible and continuous have the option of either a single continuous flexible material or multiple layers of flexible material. The need for multiple layers will not be fully determined until the selection of the final material and crease design. Some flexible materials are prone to areas of stress concentration along the folds and vertices for which holes or slits can be cut as stress relievers. In this case adhering a second layer of flexible material will maintain continuity. For products that need to be flexible and interrupted this results in a flexible material that can have cuts or slits.

Product constraints and requirements determine the general material from the four design
options. This provides foresight throughout the remainder of the design process. This concludes the problem definition phase for origami-adapted design. At this point the product requirements are known, origami is determined to be a viable design solution and the general material is selected to be a flexible, rigid, hybrid or multiple flexible materials. At this point the problem is properly defined and an origami solution can be sought.

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Modelling origami
Origami can be modelled using mathematical analysis. Mathematicians were some of the
first in the research community to develop an interest in origami 6. Demaine and O’Rourke have developed several theorems exploring the possibilities and limitations of origami, including solving origami folding problems 6. The mathematical principles explaining origami in such papers are a valuable reference for engineers in modelling and understanding origami.
Mathematical modelling is used as the basis for many origami-based design considerations
such as rigid foldability, thick origami, and defining kinematic motion (which shall be addressed
later in this work 4, 14). Articles that describe origami and its relative motion are useful for
modelling and designing origami-adapted products.

Rigid foldability
A rigidly foldable crease pattern is an origami fold pattern that can move through its full
range of motion without deformation in the panels or self-intersection. If the design uses a flexible material or is static, then rigid foldability may not be a concern. For any kinematic, rigid design, the crease pattern needs to be modified for rigid foldability. The tall, rigid shopping bag is an example of a crease pattern modified for rigid foldability. It is not always possible to adjust a crease pattern to be rigidly foldable and this requirement needs be considered when selecting an origami source model. Certain creases patterns, such as the Miura-ori crease pattern, are known to be rigidly foldable crease patterns and are used often for this reason.

Origami patterns
Current interest in deployable structures arises not only from their potential in space but also from many other areas 3–6. Several designs of origami structures have been proposed for deployable structures from around 1970s, such as the Miura-ori, which is a well-known rigid origami structure utilized in the packaging of deployable solar panels for use in space or in the folding of maps 7. Miura-ori provides a one degree-of-freedom (DOF) mechanism from a developed state to a flat-folded state.