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

Abstract

We derive new algebraic equations for the folding angle relationships in completely general degree-four rigid-foldable origami vertices, including both Euclidean (developable) and non-Euclidean cases. These equations in turn lead to novel, elegant equations for the general developable degree-four 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 new folding table design made with hyperbolic vertices has a single folding mode.

References in corpus (7)

• The designs and deformations of rigidly and flat-foldable quadrilateral mesh origami
• Origami building blocks: generic and special 4-vertices
• Non-Euclidean Origami
• Topological transitions in the configuration space of non-Euclidean origami
• On Rigid Origami II: Quadrilateral Creased Papers
• Rigid folding equations of degree-6 origami vertices
• The difficulty of folding self-folding origami