Modeling of twisted and coiled polymer (TCP) muscle based on phenomenological approach

Twisted and coiled polymers (TCP) muscles are linear actuators that respond to change in temperature. Exploiting high negative coefficient of thermal expansion (CTE) and helical geometry give them a significant ability to change length in a limited temperature range. Several applications and experimental data of these materials have been demonstrated in the last few years. To use these actuators in robotics and control system applications, a mathematical model for predicting their behavior is essential. In this work, a practical and accurate phenomenological model for estimating the displacement of TCP muscles, as a function of the load as well as input electrical current, is proposed. The problem is broken down into two parts, i.e. modeling of the electro-thermal and then the thermo-elastic behavior of the muscles. For the first part, a differential equation, with changing electrical resistance term, is derived. Next, by using a temperature-dependent modulus of elasticity and CTE as well as taking the geometry of the muscles into account, an expression for displacement is derived. Experimental data for different loads and actuation current levels are used for verifying the model and investigating its accuracy. The result shows a good agreement between the simulation and experimental results for all loads.