Non-linear quasi-static model of pneumatic artificial muscle actuators

Pneumatic artificial muscles are a class of pneumatically driven actuators that are remarkable for their simplicity, lightweight, high stroke, and high force. The McKibben artificial muscle, which is a type of pneumatic artificial muscle, is composed of an elastomeric bladder, a braided mesh sleeve, and two end fittings. Gaylord first developed an analysis of the McKibben artificial muscle based on the conservation of energy principle. The Gaylord model predicts block force but fails to accurately capture actuation force versus contraction ratio behavior. To address this lack, a non-linear quasi-static model is developed based on finite strain theory. The internal stresses in the bladder are determined by treating it as a cylinder subjected to applied internal pressure and a prescribed kinematic constraint of the outer surface. Subsequently, the force balance approach is applied to derive the equilibrium equations in both the axial and circumferential directions. Finally, the closed-form pneumatic artificial muscle quasi-static actuator force is obtained. The analysis was experimentally validated using actuation force versus contraction ratio test data at a series of discrete inflation pressures for two different pneumatic artificial muscles: a large pneumatic artificial muscle (L = 128.5 mm, B = 7.85 mm, with a latex bladder) and a miniature pneumatic artificial muscle (L = 43.9 mm, B = 2.3 mm, with a V330 elastomeric bladder).