An analytical formula for designing McKibben pneumatic muscles

The behavior of McKibben pneumatic muscles depends on the geometrical parameters, the material properties and the functional parameters. Several formulations propose relationships among the parameters in order to predict the behavior of such type of muscles. These formulations originate from theoretical or empirical models. A formulation that includes all the parameters does not exist; the existing formulations are valid for relationships among a subset of the total amount of parameters and in specific ranges of values. In this paper, an analytical formula to predict the behavior of McKibben muscles is presented. The formula expresses the relationship among the external diameter, the thickness of the inner tube, the pressure, the contraction ratio and the developed force in a convenient range of them and for a specific material used for the inner tube. The formula was achieved by an extended campaign of simulations carried out by a previously validated finite element model of the muscle. The achieved numerical results were used to define a method, here proposed, in order to replace the finite element model with the analytical formula. The validated formula can be used as a tool to design McKibben muscles starting from technical specifications, as contraction ratio and developed force, for applications of the industrial automation and soft robotics.