Generalizing rigid-foldable tubular structures of T-hedral type

TL;DR

This paper presents a novel geometric method for constructing continuous flexible tubular structures using T-hedra and profile-affine surfaces, enabling generalizations to smooth and semi-discrete tubes with isometric deformation.

Contribution

It introduces a unified geometric framework for flexible tubular structures based on T-hedra, extending to smooth and semi-discrete cases with potential applications in foldable bridges.

Findings

Generalized discrete tubes with rigid-foldability

Extended construction to smooth and semi-discrete tubes

Potential application in foldable bridge design

Abstract

We introduce an alternative way of constructing continuous flexible tubes and tubular structures based on a discrete, semi-discrete and smooth construction of surfaces known as T-hedra in the discrete case and profile-affine surfaces in the smooth setting, respectively. The geometric understanding of this method enables us to generalize discrete tubes with a rigid-foldability and to extend the construction to smooth and semi-discrete tubes with an isometric deformation. This achievement implies a unified treatment of continuous flexible structures, like surfaces and metamaterials, composed of tubes and it is the base for a deeper study of zipper tubes, and their generalization. Moreover, we discuss a potential application of the presented structures for the design of foldable bridges.