I have been researching Miura pattern origami as a structural solution for rapidly deployable structures. Miura ori are interesting as structures due to their ability to develop from a flat surface to a 3D form, and become fully rigid, with no degrees of freedom, once constrained at certain points. 
Physical and digital experiments with Miura Ori have taught me that certain topographies can be generated by developing a modified Miura pattern. With the help of Tomohiro Tachi’s excellent research on the subject of curved Miura ori, including his Freeform Origami simulator (http://www.tsg.ne.jp/TT/index.html) I have learned that Miura ori surfaces that curve in the X and Y axes can be generated by modifying the tessellating components, however these modifications require some flexibility in the material, or looseness of the hinges. 
As a system for a rapidly deployable structure, I am most interested in the potential for the modified Miura ori to work as a structure built with cheap, readily available sheet materials which are generally planar, so I will continue to develop this system as a rigid panel system with loose hinges that can be tightened after the structure is deployed. 
In order to test the crease pattern’s ability to form a curved surface, I have defined a component within the Miura pattern that can tessellate with itself. The radius of this component’s developed surface is measured as it is gradually altered.
With the objective being to develop a system for the construction of a rapidly deployable structure, I have also been interested in understanding the Miura ori’s characteristics as it is developed from flat. Physical and digital tests were performed to determine the system’s willingness to take on a curve as its crease angles decrease from flat sheet to fully developed. I found the tightest radius was achieved rapidly as the sheet was folded, with the radius angle reaching a plateau. This is interesting from the perspective of one with the desire to create a structure that has a predictable surface topography, as well as from a material optimisation standpoint; the target topography can be achieved without the wasteful deep creases of an almost fully developed Miura ori. 
With the learnings of the modified Miura ori tests in mind, a simple loose hinged cylinder is simulated. As the pattern returns on itself and is fastened, the degrees of freedom are removed and the structure is fully rigid. 
A physical model of the system was constructed with rigidly planar MDF panels and fabric hinges. The hinges were flexible enough to allow the hinge movement necessary in developing this particular modified Miura ori, however some of the panels’ corners peeled away from the fabric backing as the system was developed from flat. A subsequent test will seek to refine this hinge detail, with a view to creating a scalable construction detail that will allow sufficient flexibility during folding, as well as strength once in final position. 
John Konings
j.e.konings@gmail.com
WeWantToLearn.net 