A Thickness-Accommodated, Self-Deployable Parabolic Origami Flasher

Origami folding principles are increasingly applied to design high-gain antenna reflectors, with origami flasher emerging as a leading pattern for its notable deploy-to-stow ratio. Yet, existing work lacks a comprehensive approach for designing deployable parabolic origami flashers that account for material thickness and actuation details. To bridge this gap, we introduced a systematic way to design thick parabolic origami reflectors, incorporating material thickness in the folding pattern design. Through kinematic simulations, we discerned the loading conditions for folding the flasher. Using these simulation results, we designed a self-deployable truss framework to guide the deployment of parabolic flasher by integrating compliant leaf springs into an optimized Hoberman ring. To validate our design methodology, we prototyped a hexagonal-centered six-layer parabolic flasher using polyethylene terephthalate (PET) plates and thermoplastic polyurethane (TPU) film, mimicking the mechanical properties of antenna reflectors. Our design method introduces a surface approximation error constrained within 7.62%, showcasing a high accuracy. Comparison of the stowed form with integrated trusses to the deployed flasher without truss framework revealed deploy-to-stow ratios of 1.90 and 3.60 for diameter and area, respectively. The proposed method holds significant potential for designing large-scale deployable parabolic antennae in aerospace to save storage and launching costs.