This paper investigates the geometry of a foldable barrel vault with modified Miura-ori patterns, which displays a curvature during the motion. The principal of spherical trigonometry was used to obtain the relationship of the inclined angles between adjacent folded papers of Miura-ori. Then, the radius, span, rise, and longitudinal length of the foldable barrel vault in all configurations throughout the motion are determined. The results show that the radius of curvature grows exponentially and the span increases during deployment. Furthermore, the rise increases first, followed by a decrease with increasing deployment angle.
Geometric Analysis of a Foldable Barrel Vault With Origami
Contributed by the Design Innovation and Devices of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 8, 2012; final manuscript received August 14, 2013; published online September 24, 2013. Assoc. Editor: Alexander Slocum.
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Cai, J., Xu, Y., and Feng, J. (September 24, 2013). "Geometric Analysis of a Foldable Barrel Vault With Origami." ASME. J. Mech. Des. November 2013; 135(11): 114501. https://doi.org/10.1115/1.4025369
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