We derive algebraic equations for the folding angle relationships in completely general degree-4 rigid-foldable origami vertices, including both Euclidean (developable) and non-Euclidean cases. These equations in turn lead to elegant equations for the general developable degree-4 case. We compare our equations to previous results in the literature and provide two examples of how the equations can be used: in analyzing a family of square twist pouches with discrete configuration spaces, and for proving that a folding table design made with hyperbolic vertices has a single folding mode.

Explicit kinematic equations for degree-4 rigid origami vertices, Euclidean and non-Euclidean

Riccardo Foschi
Co-primo
;
2022

Abstract

We derive algebraic equations for the folding angle relationships in completely general degree-4 rigid-foldable origami vertices, including both Euclidean (developable) and non-Euclidean cases. These equations in turn lead to elegant equations for the general developable degree-4 case. We compare our equations to previous results in the literature and provide two examples of how the equations can be used: in analyzing a family of square twist pouches with discrete configuration spaces, and for proving that a folding table design made with hyperbolic vertices has a single folding mode.
2022
Riccardo Foschi, Thomas C. Hull, and Jason S. Ku
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/900422
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