To enable a new class of in-space deployable antennas and reflectors, we are developing an approach for creating expandable parabolic shells based on an origami structure known as a "flasher". Building upon an existing planar flasher design approach, three new methods to generate parabolic surfaces are under investigation. Each method offers a set of modifications to the origami facets generated for a planar structure, to result in a targeted out-of-plane parabolic geometry. Development takes place within a 3D CAD environment, where the patterns are algorithmically dissected, modified, reassembled, and then assessed for parabolic shape accuracy. Inter-panel gaps are added to guarantee closure to a folded state without the occurrence of self-intersecting geometry. A shape error approximation is proposed and reported for the resulting structures. The CAD environment also allows for assessment of each structure's foldability, which is the ease with which the structure can transform from the compact stowed state to the fully deployed state. Based on the results generated in CAD, physical models are constructed to validate the results. Initial results indicate a stark tradeoff between shape capability and rigid working area.
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