An Elastica Arm Scale

The concept of a ‘deformable arm scale’ (completelydifferent from a traditional rigid arm balance)istheoreticallyintroducedandexperimentallyvalidated. The idea is not intuitive, but is the resultof nonlinear equilibrium kinematics of rods inducingconfigurational forces, so that deflection of the armsbecomes necessary for equilibrium, which would beimpossible for a rigid system. In particular, the rigidarms of usual scales are replaced by a flexible elasticlamina, free to slide in a frictionless and inclinedsliding sleeve, which can reach a unique equilibriumconfiguration when two vertical dead loads areapplied. Prototypes designed to demonstrate thefeasibility of the system show a high accuracy inthe measurement of load within a certain range ofuse. Finally, we show that the presented results arestrongly related to snaking of confined beams, withimplications for locomotion of serpents, plumbingand smart oil drilling.