Modeling of TCP Muscles for Understanding Actuation Behavior

Twisted and Coiled Polymers (TCP) muscles are actuators that generate force and linear displacement in response to thermal stimuli. Their length changes significantly by heating due to a high negative coefficient of thermal expansion (CTE). A mathematical model for predicting the behavior of TCP muscles is essential for exploiting maximum advantage from these actuators and also controlling them. In this work, a simple, practical, and accurate model for predicting the displacement of TCP muscles, as a function of input electrical actuation and load, is derived. The problem is broken down into two, i.e. modeling of the thermal and thermo-elastic part. For the first part, a differential equation with changing electrical resistance term is derived. In the next step, by using a temperature-dependent modulus of elasticity and CTE as well as taking the geometry of muscles into account, an expression for displacement as a function of temperature and load is proposed. Experimental actuation data of a TCP muscle is used for verifying the model and investigating its accuracy. The thermal part shows a good agreement between the simulation and experimental result. The displacement part also has a good accuracy for medium and high actuation currents but there is a mismatch in very high current magnitudes. The cause of the discrepancy is explained and recommendations are made for the best performance of TCP muscles.