Multi-stable design of triangulated origami structures on cones of revolution

TL;DR

This paper generalizes multi-stable origami structures based on Kresling patterns from cylinders to cones, enabling design of snap-through conical origami with controllable apex angles and analyzing their stability and self-intersection properties.

Contribution

It introduces a novel approach to design multi-stable origami on conical surfaces, extending previous cylindrical models and analyzing their stability and geometric constraints.

Findings

Structures can snap between different conical configurations.

Intervals for self-intersection free realizations are identified.

A snappability index quantifies the structures' ability to snap.

Abstract

It is well-known that the Kresling pattern of congruent triangles can be arranged either circularly on a cylinder of revolution or in a helical way. In both cases the resulting cylindrical structures are multi-stable. We generalize these arrangements with respect to cones of revolution, where our approach allows to construct structures, which snap between conical realizations whose apex angles serve as design parameters. In this context we also figure out shaky realizations, intervals for self-intersection free realizations and an interesting property related to the cross sectional area. Finally, we analyze these origami structures with respect to their capability to snap by means of the so-called snappability index.