Characterization and modeling of geometric variations in McKibben pneumatic artificial muscles

This paper presents experimental data on the actuation properties of McKibben muscles constructed with varying bladder pre-strain and thickness. The tests determine quasi-static force-length relationships during extension and contraction, for muscles constructed with unstretched bladder lengths 50%, 67%, and 100% of the stretched muscle length, as well as two different wall thicknesses of the rubber. Existing models do not adequately describe the effects of these variations, making it difficult to determine the best geometry for an application. The quasi-static actuator force and maximum contraction length are found to depend strongly on the thickness and modulus of the rubber, as well as the amount of pre-strain. A model is presented to better predict force-length characteristics from geometric parameters. It accounts for the nonlinear elastic properties of the bladder as well as friction. It includes axial force generated by stretching the bladder during construction, and it also describes the hoop stress created by radial expansion of the bladder, which partially counteracts the internal fluid pressure that presses outward on the mesh, thus reducing both axial force and friction between the mesh and bladder. The hyperelastic rubber bladder is modeled as a Mooney-Rivlin incompressible solid. The axial force generated by the mesh is found directly from contact forces rather than from potential energy. The model closely matches the experimental data on wall thickness, while the effects of bladder pre-stretching are not fully explained. A thick-walled bladder model is shown to improve the fit.