Mechanics of tubular meshes made of helical fibers and application to modeling McKibben artificial muscles

Abstract

McKibben artificial muscles are an important example of braided, tubular structures made of many interwoven helical fibers. Despite their high non-linearity, the elastic response of these soft pneumatic actuators is very robust and reproducible, making them particularly suitable for applications in Soft Robotics. The rich behavior of McKibben actuators has been studied either through minimal geometric models or through complex Finite Elements Methods (FEM).Here, we develop a simplified framework entirely based on the virtual envelope surface defined by the fibers of the mesh. In the axisymmetric cases studied, the problem boils down to solving for a single scalar field defined over 1D segments. We then validate our model against experimental and numerical results from the literature, achieving a good agreement at a significantly lower computational cost. Furthermore, simulations reveal that loads are sustained mostly by the braided mesh, whereas the inner chamber stores as elastic energy most of the external work. This phenomenon explains why simplified formulas for force-pressure relationship may be quite effective in predicting the behavior of McKibben actuators.