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

McKibben artificial muscles are an important example of braided, tubular structures made of many interwoven helical fibers. Their highly non-linear response 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 Method (FEM) simulations. To obtain a simpler yet accurate model for McKibben actuators, we develop a simplified framework entirely based on the geometry of the virtual envelope surface defined by the fibers of the mesh. In the axisymmetric cases studied here, the problem boils down to solving for a single scalar field of one scalar variable. We validate our model by solving contractor and extensor muscle configurations and comparing them against experimental and numerical results from the literature, achieving good agreement at a significantly lower computational cost. Simulations reveal that loads are sustained mostly by the braided mesh, whereas the inner chamber stores most of the external work as elastic energy. This phenomenon explains why simplified formulas for force-pressure relationship may be quite effective in predicting the behavior of McKibben actuators.