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The paper introduces a geometric construction method for bistable mechanical structures composed of spatial four-bar linkages, leveraging their interpretation as quad nets in the Study quadric. The approach uses Whiteley de-averaging applied to infinitesimally flexible quad nets in Euclidean space, providing a purely geometric alternative to numerical optimization. This enables the creation of arbitrarily large bistable structures, including those derived from discrete minimal surfaces, with control over axis positions and snap angles.
Unlock bistable mechanical designs without optimization: a geometric construction using quad nets offers unprecedented control over structure and behavior.
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.