Physics-based modeling of twisted and coiled artificial muscles (TCAMs) for soft robotics using extended Cosserat theory of rods

Abstract The current work develops a physics-based model for twisted and coiled artificial muscles (TCAMs) using the extended Cosserat theory of rods. These artificial muscles are lightweight and low-cost, generating a high power-to-weight ratio. They produce tensile forces up to 12 600 times their own weight, closely mimicking the functionality of biological muscles. The contraction of these muscles is driven by the anisotropic volume expansion of their twisted fibers, induced by deformation of the fibers’ cross-section. Unlike prior models, this study implements the extended Cosserat theory, which models not only rigid rotations (like standard Cosserat theory) but also planar anisotropic deformation of the TCAMs’ cross-section. The static deformation and dynamic motion of TCAMs are formulated herein. The governing equations for the bulk deformation of TCAMs are derived through standard Cosserat rod theory, while a continuum mechanics approach is utilized to model the cross-sectional deformation. The Bernstein polynomial method is applied to discretize the continuous formulations, enabling numerical solutions to the problem. Experimental datasets are used for evaluation of the models.