Modelling of the McKibben artificial muscle: A review

The so-called McKibben artificial muscle is one of the most efficient and currently one of the most widely used fluidic artificial muscles, due to the simplicity of its design, combining ease of implementation and analogous behaviour with skeletal muscles. Its working principle is very simple: The circumferential stress of a pressurized inner tube is transformed into an axial contraction force by means of a double-helix braided sheath whose geometry corresponds to a network of identical pantographs. However, behind this apparent simplicity lie two phenomena, which must be considered so as to fully understand how the McKibben muscle works. First, the non-linear relationship between stress and strain inside the inner tube elastomer, together with the complex relationship between physical artificial muscle parameters and its effective working pressure range. Second, the behaviour of the braided sheath which acts like a ‘flexible joint structure’ able to adapt itself during contraction to the increasing radius muscle in its middle portion, with the boundary constraint of rigid tips. By distinguishing an ideal model with a zero inner tube thickness from a real model with a non-zero inner tube thickness, we attempted to synthesize static models by including and excluding an elastic force component. However, we also highlight the possible need, in further modelling, to distinguish modelling thin-walled from thick-walled inner tube McKibben muscles. In our attempt to understand the hysteresis peculiar to the muscle, it seems, resulting from our review, that this hysteresis phenomenon is essentially due to strand-on-strand friction inside the weave. Nevertheless, although Hertz’s contact theory has shown its relevance in tackling this problem, friction modelling in a McKibben muscle is particularly hard due to the difficulties, first, to correctly determine the real contact surface strand-on-strand and, second, to estimate the friction coefficient and its possible dependence on pressure and velocity with the weaving peculiar to McKibben braided sheaths. We propose in a future approach to better integrate textile physics into this very complex modelling problem. Moreover, because we consider friction to be velocity-dependent, a distinction between static and dynamic modelling appears necessary to us and can help, in our view, towards a better understanding of the Hill-like character (or not) debate concerning artificial muscles.