Explicit kinematic equationsfor degree-4 rigid origami vertices, Euclidean and non-Euclidean.

Abstract

We derive algebraic equationsfor the folding angle relationships in completely general degree-4 rigid-foldable origami vertices, including both Euclidean (developable) and non-Euclidean cases. These equationsin turn lead to elegant equationsfor the general developable degree-4 case. We compare our equationsto previous results in the literature and provide two examples of how the equationscan 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.