Fiber-Reinforced Membrane Models of McKibben Actuators

A McKibben actuator consists of an internally pressurized elastic cylindrical tube covered by a shell braided with two families of inextensible fibers woven at equal and opposite angles to the longitudinal axis. Increasing internal pressure causes the actuator to expand radially and, due to the fiber constraint, contract longitudinally. This contraction provides a large force that can be used for robotic actuation. Based on large deformation membrane theory, the actuator is modeled as a fiber-reinforced cylinder with applied inner pressure and axial load. Given the initial shape, material parameters, axial load, and pressure, the analytical model predicts the deformed actuator shape, fiber angle, and fiber and membrane stresses. The analytical results show that for a long and thin actuator the deformed fiber angle approaches $54°44′$ at infinite pressure. The actuator elongates and contracts for actuators with initial angles above and below $54°44′$ degrees, respectively. For short and thick actuators with initial angles relatively close to 0 deg or 90 deg, however, a fiber angle boundary layer extends to the middle of the actuator, limiting possible extension or contraction. The calculated longitudinal strain and radius change match experimental results to within 5%.