A constrained maximization formulation to analyze deformation of fiber reinforced elastomeric actuators

Fiber reinforced elastomeric enclosures (FREEs) are soft and smart pneumatic actuators that deform in a predetermined fashion upon inflation. This paper analyzes the deformation behavior of FREEs by formulating a simple calculus of variations problem that involves constrained maximization of the enclosed volume. The model accurately captures the deformed shape for FREEs with any general fiber angle orientation, and its relation with actuation pressure, material properties and applied load. First, the accuracy of the model is verified with existing literature and experiments for the popular McKibben pneumatic artificial muscle actuator with two equal and opposite families of helically wrapped fibers. Then, the model is used to predict and experimentally validate the deformation behavior of novel rotating-contracting FREEs, for which no prior literature exist. The generality of the model enables conceptualization of novel FREEs whose fiber orientations vary arbitrarily along the geometry. Furthermore, the model is deemed to be useful in the design synthesis of fiber reinforced elastomeric actuators for general axisymmetric desired motion and output force requirement.