Parametrically Excited Nonlinear Pneumatic Artificial Muscle Under Hard Excitation: A Theoretical and Experimental Investigation

In this work, a single degree of freedom system consisting of a mass and a Pneumatic Artificial Muscle subjected to time-varying pressure inside the muscle is considered. The system is subjected to hard excitation and the governing equation of motion is found to be that of a nonlinear forced and parametrically excited system under super- and sub-harmonic resonance conditions. The solution of the nonlinear governing equation of motion is obtained using the method of multiple scales. The time and frequency response, phase portraits, and basin of attraction are plotted to study the system response along with the stability and bifurcations. Further, the different muscle parameters are evaluated by performing experiments which are further used for numerically evaluating the system response using the theoretically obtained closed form equations. The responses obtained from the experiments are found to be in good agreement with those obtained from the method of multiple scales. With the help of examples, the procedure to obtain the safe operating range of different system parameters is illustrated.