Bistable Quad-Nets Composed of Four-Bar Linkages

TL;DR

This paper introduces a geometric method to construct bistable spatial four-bar linkage structures, connecting discrete differential geometry with practical design of large, controllable bistable mechanisms.

Contribution

It presents a novel purely geometric construction method for bistable quad-net structures using Whiteley de-averaging, without numerical optimization.

Findings

Constructed large bistable structures from quad nets in the Study quadric.

Enabled control over axis positions and snap angles in the structures.

Linked discrete differential geometry with practical bistable mechanism design.

Abstract

We study mechanical structures composed of spatial four-bar linkages that are bistable, that is, they allow for two distinct configurations. They have an interpretation as quad nets in the Study quadric which can be used to prove existence of arbitrarily large structures of this type. We propose a purely geometric construction of such examples, starting from infinitesimally flexible quad nets in Euclidean space and applying Whiteley de-averaging. This point of view situates the problem within the broader framework of discrete differential geometry and enables the construction of bistable structures from well-known classes of quad nets, such as discrete minimal surfaces. The proposed construction does not rely on numerical optimization and allows control over axis positions and snap angles.