Nonlinear dynamics of twisted and coiled polymer actuator made of conductive nylon based on the energy balance

This paper proposes a novel dynamics model of the twisted and coiled polymer actuator (TCPA) which is one of the artificial muscles recently discovered. It can be driven by Joule heating and can contract up to 25%. Most of the conventional works employed the linear model of TCPA which represents the relationships between the input voltage, the temperature, and the displacement, but the real TCPA shows the nonlinearity. Although a nonlinear model was proposed based on the curve fitting, it is difficult to apply the model to the various TCPAs. Additionally, the conventional works cannot explain the effect of the convective heat transfer condition on the displacement behavior of TCPA. This paper aims to construct a general nonlinear model of TCPA based on the following two ideas: (1) The energy balance of TCPA and (2) the temperature and velocity dependence of the heat transfer coefficient. The temperature model is obtained from the time derivative of the energy balance, and the displacement model is derived as Lagrange's equation of motion with the dissipation function. Through experiments, it is verified that the proposed model is closer to the real dynamics than the conventional linear model.

I. Introduction

It is expected to apply the robotics to the welfare field such as the rehabilitation, the prosthesis, and the motion assistance. Actuators for them are required to be soft in order not to injure humans when the contact occurs, while those are necessary to be powerful to support their motion. The twisted and coiled polymer actuator (TCPA [1]–[3]), which is also known as the fishing line artificial muscle [4], [5], the coiled fishing line actuator [6], the super-coiled polymer actuator [7], the nylon actuator [8] and so on, is one option of such actuator. TCPA is fabricated by twisting polymer fibers such as nylon and polyethylene, and contracts by heating [4]. Its stroke is up to 25 %, and its specific power runs up to 5.26 kW/kg, which is over 100 times as large as that of human muscle. Additionally, there is less hysteresis than the shape-memory-alloy (SMA) which is driven by heating as well as TCPA.