  Twisted and coiled polymer actuators (TCPAs) generate large contractile
mechanical work mimicking natural muscles, which makes them suitable for
robotics and health-assistive devices. Understanding the mechanism of nylon
TCPA remains challenging due to the interplay between their intricate geometry,
chirality, residual stresses, and material microstructure. This study
integrates a material microstructure model with rod theory to analytically
predict the equilibrium helical shape of the nylon TCPA after fabrication and
to explain the observed contraction mechanism upon stimulation. The first
ingredient of the model is to treat nylon as a two-phase thermomechanical
microstructure system capable of storing strain energy and exchanging it among
the two phases. This is validated by characterizing the torsional actuation
response of twisted and annealed nylon fibers. The second ingredient of the
model is to use the classic Kirchhoff Rod Theory and add a necessary term that
couples the bending and twisting energy. Validation with experiments shows that
the model captures the equilibrium and longitudinal stiffness of the TCPA in
both active and passive states, and the stimulated contraction under external
load. Importantly, the model quantifies the influence of the stored energy
level on the actuation performance. These concepts can be extended to other
types of TCPAs and could enable new material design.
