Enhanced static modeling of commercial pneumatic artificial muscles

1. Introduction

As the pneumatic artificial muscles (PAM) ;(also known as Mckibben muscle) was invented to actuate an orthotic device for helping control handicapped hands in the 1950s (Pierce, 1940), it has been widely adopted in the field of robotics from biomimetic robots (Zhong et al., 2012) to motion simulation platforms (Zhao et al., 2018), inspection robots (Takeichi et al., 2017) and wearable exoskeletons (Kurumaya et al., 2016). Particularly, the merits of safety and low cost prompt PAMs to be promising for rehabilitation. Recent achievements in fabrication, modeling and control methods have significantly facilitated their numerous applications (Zhang et al., 2019).

A PAM generally consists of a rubber bladder surrounded by helically braided strands, which combines the characteristics of compliance and high force-to-weight ratios as compared to human body muscles. Once the bladder is pressurized, the high-pressure gas pushes against its inner face to increase the volume. Owing to the high longitudinal stiffness of the braids, the PAM contracts along with generating tension. On the contrary, it returns to the original length approximately when the applied pressure is released.

The mathematical static models of PAMs relate the contraction force to the contraction ratio and the applied pressure. Gaylord (1958) performed the first PAM force analysis in his early work. Chou and Hannaford (1996) derived a model via considering the volume change on the principle of virtual work and arrived at the same expression of Gaylord. Nevertheless, this model was derived assuming that it retained cylindrical close to the end-fittings during inflation, none elastic energy was stored in the bladders and the braids and none friction existed. Consequently, the static model can be written as follows: (1) $$F=\frac{\pi D_0^{2}p}{4}(3co{s}^2\theta -1)$$where p denotes the muscle pressure, θ denotes the braid angle of the braided strands, D₀ denotes the outer diameter of the PAM with the braid angle of 90° and F denotes the contraction force. This model laid the foundation for almost all the modified models that contain all kinds of compensatory terms. Distinctively, this model neglected the hysteresis effect that was first modeled by an experimentally determined force offset (Chou and Hannaford, 1996)....

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