Origami for Engineers

"At a slight angle to the universe."
Em Foster on poet 'CP Cavafy'

    Nature likes things that can fold away into something small and open out when they are needed. Engineers call these things deployable structures. The umbrella is a perfect example of this. When you press a button, the shaft expands and with doing so the forces help open the spokes that carry the fabric. An umbrella may be a perfect example of a deployable structure but it also shows the key problem with a deployable structure which is that it is not fully automatic. When it opens, the fabric begins to tighten which creates a dramatic increase of force to push it all the way and lock it into place. Once it's locked, you have to apply even more force to be able to unlock it and fold it back up again. Engineers call this a bistable system, which means that changing from one state to another can be difficult. It is hard to design a system that can be fully automatic on its own but it seems that nature has already figured it out. A beetles wing's are a deployable structure because they unfold and open fairly easy and then fold up again when they are not in use.
    In human nature we tend to fold things at right angles. It has come to the point that if we did not fold newspapers or letters at a right angle then we usually create a problem with how these papers are displayed. There is nothing wrong with this but human nature is always about finding an easier way to do things. If we can mimic the folds from a hornbeam and beech leaf then that could be possible. If you were to look at a leaf bud from these trees you wold notice that the bud is much smaller than what the leaf will become. How can something so tightly packed expand in both length and width as it grows? It comes down to the folding techniques that is used. This origami is known as Ha-ori (meaning 'leaf-fold'). It can unfold with just one pull and even though it does not fold up as easily, it makes a good attempt. This is a good example of bistability. The leaf folding pattern was discovered by Biruta Kresling. She learned how to paper fold from Koryo Miura, a Japanese expert in folding structures.
    Miura was not only an expert in folding structures but he was also a Japanese space scientist. His ideas of folding influenced his work in space science. Miura saw a crumpling pattern when you crumble a piece of paper, the paper was now in three dimensions. By 1978, Miura had a general theory of how to collapse a piece of paper. He wanted to apply it to folding solar pannels. He initially described his technique as a 'Developable Double Corrugation Surface' but also became known as Miura-ori.

    Miura-ori helped develop solar panel arrays for space satellites. Solar panels need as much surface area as possible to increase the energy produced. But to be launched into space they need to be a lot smaller. In Miura's space arrays, the panels have the same shape and angles as the paper-folds but since there is no one in space to pull the panels they needed joints and tension strut to manipulate them. Such an array went into space on March 18, 1995.

Below is a video on how to do a Miura-ori fold