Modeling and Design of “Smart Braid” Inductance Sensors for Fiber-Reinforced Elastomeric Enclosures

Fiber-reinforced soft actuators use inextensible fibers to shape the expansion of elastomeric fluid-filled chambers. The classic example, McKibben muscles, is part of a broader class of cylindrical soft actuators known as fiber-reinforced elastomeric enclosures (FREEs). These actuators can be designed to twist while extending or contracting. Using a circuit of conductive, electrically insulated wire as the reinforcing fibers allows one to measure the motion of the actuator with the circuit inductance. These sensors, developed previously for McKibben muscles, are known as “Smart Braids.” This paper extends the concept of Smart Braids to the broader class of two-fiber-family cylindrical FREEs. A dimensionless model for the inductance of Smart Braid FREEs is presented that can be scaled to specific sensor geometries. This model depends only on the ratio of the fiber lengths in the two families and the angle of one of the fibers. The model was validated both numerically and experimentally, predicting the sensitivity of experimental sensors accurately, the largest errors being -11% and 9%. The model presented in this paper will enable high-level design decisions for Smart Braid FREES and optimization without computationally expensive direct numerical simulation.