A mechanical model for McKibben pneumatic artificial muscles based on limiting chain extensibility and 3D application of the network alteration theories

Abstract

Pneumatic Artificial Muscles (PAMs) mimic the behavior of skeletal muscles by generating contractile force when they are pressurized. Stiffness of these actuators depends on the applied pressure because the inner elastomeric tube exhibits non-linear mechanical behavior which also makes control of the actuator difficult. Therefore, it is crucial to obtain a precise mechanical model for these actuators. In this work, based on the theory of limiting chain extensibility, a new continuum mechanics-based model is developed for elastomeric McKibben PAMs to predict stiffness and output parameters such as free contraction, blocked force, and dead-band pressure during the actuation course. The developed model is consistent with network alternation theories, which allow predicting the softening observed in first cycles of inflation-deflation (Mullins effect). The established relations can predict variations of the actuation force due to the alternation of the material network parameters as a result of Mullins softening. In order to determine the material parameters of the bladder, uniaxial tensile tests have been conducted on a virgin silicon rubber. Cyclic tests have also been conducted on the fabricated PAMs in virgin and completely softened states to obtain their characteristic curves. It is concluded that, fractional evolution laws can be well combined with the developed model to predict the behavior of PAMs during cyclic deformations. It is observed that, even for contractions less than 25%, the maximum principal stretch in a PAM can exceed three which implies that, simple strain energy functions such as NeoHookean and Mooney-Rivlin should not be employed for PAMs. It is also concluded that, the Mullins softening increases the free contraction while makes no remarkable effect on the blocked force.