Theory of the tensile actuation of fiber reinforced coiled muscles

There is a strong need for compact artificial muscles capable of applying large contractile strokes and lift heavy weights. Coiled fibers recently emerged as attractive candidates for these purposes, owing to their simple construction and the possibility of their thermal, electrical and chemical actuation. An intuitive theoretical understanding of the mechanics of actuation of these muscles is essential for the enhancement of their performance and can pave the way for the development of new applications and technologies. In this paper, a complete theoretical model for the tensile actuation of fiber reinforced artificial muscles is presented and experimentally validated. The model demonstrates that all muscles made from the same material have a universal behavior, which can be described by a single master curve. It enables the systematic design and understanding of coiled muscles for specific performance owing to a comprehensive mathematical correlation among the geometry, materials properties, and actuation. Carbon fibers (CF)/polydimethylsiloxane coiled muscles are demonstrated as simple to fabricate yet powerful muscles owing to the availability of high strength CF. In addition to showing excellent agreement with the theoretical models, they can be actuated by joule heating or chemical swelling, lift up to 12 600 times their own weight, support up to 60 MPa of mechanical stress, provide tensile strokes higher than 25%, and a specific work up to 758 J kg^-1, the latter is more than 18 times higher than that of natural muscles.