Numerical modeling of cantilevered bigon arm mechanics under gravity

Elastic Rod Networks (ERNs) formed from interconnected slender, elastic rods can undergo large nonlinear displacements, resulting in phenomena like multi-stability and increased geometric stiffness. By varying the networks’ physical properties and boundary conditions, ERNs can be tailored for applications in mechanical metamaterials, aerospace engineering and soft robotics. Bigon arms are a type of multi-stable ERN composed of bistable bigon units, which are made up of two flat and slender strips, joined at prescribed intersection angles. The global geometry of bigon arms may be tuned by varying the individual units’ strip length, width-to-thickness ratio and intersection angles. Bigon arms can be utilized in reconfigurable structures, for example acting as grippers or moving autonomous robotic systems. However, the configuration space of fixed-angle bigon arms has not been explored in depth, and the influence of gravity on their mechanical behavior has not yet been investigated. In this study, we address this knowledge gap for bigon arm design by formulating a Boundary Value Problem (BVP) to model the displacements of bigon arms under gravity loading. The numerical simulations are validated with decimeter scale physical models. Our results unveil three distinct regions for the bigon arm mechanical behavior: a stable region, a multi-stable region, and one transitionary region connecting the first two. Ultimately, this study provides insights of the parameters influencing the design of adaptive bigon arms and offers an outlook for their future design development.