On the coupling of non-linear inflatables and springs: Island-hopping

Mechanical elements that deform in response to an input effort, such as linear springs (force-displacement), torsional springs (torque-rotation), and inflatable volumes (pressure-volume), often display non-linear responses. In mechanical systems, these non-linear elements can be coupled in series, where all experience the same effort, or in parallel, where they share the same deformation, to achieve complex desired responses. However, there is currently no analytical solution to describe the coupling of arbitrary non-linear elements. In this talk, we introduce a novel technique for analyzing systems of N-coupled mechanical elements through parametrizing their effort-deformation curves. This method enables the determination of all equilibrium points of the system, including undetermined (bifurcations) and isolated (islands) solutions, offering new insights into the behavior of the system. Additionally, we propose an island-hopping method, where dissipative elements, such as dampers or flow restrictors, are incorporated to temporarily disrupt equilibrium between components, allowing transitions between islands. Next, we examine the stability of coupled systems based on component stability and the influence of interactions (series coupling) or constraints (parallel coupling). In addition to system analysis, the proposed technique can be applied to the synthesis of complex mechanical behaviors by combining multiple simple components.