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Prototyping soft origami quad-bellows robots from single-bellows characterization 25

               the snake undergo this process, the contraction wave will travel posteriorly such that the
               snake can slowly move forward in a rectilinear manner [24].


               2.3.1.2 Snake’s concertina locomotion
               Snakes usually use concertina locomotion in tunnels, especially ones with smooth surfaces,
               in which the snake’s movements that usually rely on large areas of friction are not suitable.
               This type of locomotion requires a snake to keep bending and straightening its body, as it
               anchors part of its body while pulling the rest of its body in the direction of motion so that
               it can “climb” and progress forward. The reason for the multiple tight bending loops is to
               increase anchor points to achieve enough friction to brace itself before it can push forward
               to straighten to the next anchor point. In tunnels that are inclined, snakes can change the
               orientation of their scales to increase anchorage by digging into the surface to prevent
               slipping due to gravity [25].

               Snakes often use rectilinear, and concertina locomotion, either combined or separately,
               to climb surfaces, and both types of movement are similar in their ability to move
               through narrow spaces. Thus both types of movement are beneficial and relevant to
               biomedical applications such as colonoscopy. Concertina motion is beneficial for curved
               trajectory advancement, and rectilinear locomotion is applicable for an end-effector
               advancement as well as providing an alternative to the techniques such as jiggling to
               prevent entanglement. However, a point to note is that a certain amount of friction is
               necessary to enable the snake to be able to utilize these movements to move forward or
               through tunnels.

               2.3.2 Bellows design


               In the process of deciding what type of origami folding would be best for this project, the
               Miura or Kresling fold [26], bistable origami were considered with slight modifications, but
               the simple octagonal bellows design has its simplicity and applicability.

               2.3.2.1 Origami pattern

               The current prototype robot design is composed of multiple identical units based on the
               simple octagonal bellows origami pattern shown in Fig. 2.1. The full origami layout seen on
               the left of Fig. 2.1 shows how the flat material was creased into the appropriate alternating
               mountain and valley folds. The creased material was then folded to form the 3D bellows
               structure displayed on the right of Fig. 2.1. Fig. 2.2 shows a close-up look at the hexagon
               pattern used to fold the octagonal bellows structure. The protruding three squares on the top
               and bottom of the origami layout in the left of Fig. 2.1 are necessary to close the gap that
               arises from only folding duplicates of the basic origami pattern so that the folded 3D
               structure is ready to be glued and coated with silicone for use.
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