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Title: Rigid folding equations of degree-6 origami vertices
Rigid origami, with applications ranging from nano-robots to unfolding solar sails in space, describes when a material is folded along straight crease line segments while keeping the regions between the creases planar. Prior work has found explicit equations for the folding angles of a flat-foldable degree-4 origami vertex and some cases of degree-6 vertices. We extend this work to generalized symmetries of the degree-6 vertex where all sector angles equal 60 ∘ . We enumerate the different viable rigid folding modes of these degree-6 crease patterns and then use second-order Taylor expansions and prior rigid folding techniques to find algebraic folding angle relationships between the creases. This allows us to explicitly compute the configuration space of these degree-6 vertices, and in the process we uncover new explanations for the effectiveness of Weierstrass substitutions in modelling rigid origami. These results expand the toolbox of rigid origami mechanisms that engineers and materials scientists may use in origami-inspired designs.  more » « less
Award ID(s):
1906202
NSF-PAR ID:
10321491
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume:
478
Issue:
2260
ISSN:
1364-5021
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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