Developable Membrane Tensegrity Structures Based on Origami Tessellations

In this paper, we propose a design method of membrane tensegrity structures by solving the inverse problem using freeform origami tessellations by generalizing Resch’s patterns. We found that if we generate an origami tessellation and replace the mountain crease of the tessellation with struts and the other parts with a membrane under initial tension, the tessellation can be formed as a tensegrity structure. In addition, this structure may snap through and deform significantly, but we have shown that the mean curvature of a given surface is a valid evaluation index as a condition for a surface that does not snap through. When computed origami tessellation patterns are naively used, the shrinking of membranes caused by initial tension results in a deviation from the target shape.We propose an optimization-based framework that resolves the deviation and ensures that the structures match the given surfaces.