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.

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