## 2 Materials and Methods  
### Working Principles of Variable Thickness MRF Transmission Device  
The working principles of the variable thickness MRF transmission device actuated by electrothermal SMA are shown in Figure 1. This MRF transmission device mainly consists of components such as an input shaft, output shaft, squeeze disc, rotary housing, electrothermal SMA spring, guide disc, and excitation coil. The electrothermal SMA spring is positioned on the guide plate, and the two ends of the spring are respectively connected with the rotary housing and the guide plate in a fixed manner. The output shaft is bolted to the rotary housing, the guide disc and the squeeze disc are connected by the bolts, and the brush slip ring is at the shoulder of the output shaft. The wires of the brush slip ring are connected to the excitation coil and the electrothermal SMA spring, respectively, through the wire holes on the rotary housing, and the power is supplied to the coil and the electrothermal SMA spring, respectively, through the external slip ring. The MRF is filled between the rotary part of the input shaft and the squeeze disc, which is sealed by sealing rings on each side. For the purpose of changing the thickness of the working gap of the MRF transmission device during operation, a squeeze disc is installed between the disc area of the input shaft and the rotary housing, and the squeeze disc is propelled by the displacement or force output by the electrothermal SMA spring during the temperature rise, thereby enabling changes in the distance of the MRF working gap formed by the squeeze disc and the disc area of the input shaft, so that the process of changing the thickness of the MRF working gap can be controlled by an applied current.  
The operating principles of the electrothermal SMA spring-driven variable thickness MRF transmission device are as follows:  
1. Under the initial condition, when the coil is not energized, the MRF is in zero-field state, and the input shaft cannot drive the output shaft to rotate only by the shear stress generated by the MRF zero-field viscosity during the rotation.
2. When the transmission device starts to function, the excitation coil is energized to generate a magnetic field, the magnetic particles in the MRF are arranged in a chain along the magnetic flux direction, the shear yield stress is significantly enhanced, and the output shaft is rotated by this shear yield stress; furthermore, as the coil current increases, the transmission torque of the device can be further increased.
3. To further increase the torque of the MRF transmission device, by loading the electrothermal SMA spring with current, the Joule heat generated by the current generates a shape memory effect in the SMA, and the force or displacement generated by the  
Figure 1: Working principles of MRF transmission device. (**a**) 2D structure diagram and (**b**) 3D structure diagram.  
electrothermal SMA drives the squeeze disc to gradually start squeezing the MRF working gap thickness from 1.5 mm, and the axial squeeze increases the MRF shear yield stress exponentially. As a result, the transmission torque of the MRF transmission device is further increased.
4. At the end of the operation, the excitation coil is de-energized and the MRF is restored to a Newtonian fluid upon the disappearance of the magnetic field by the viscoplastic body, and the electrothermal SMA spring gradually regains its original length as the temperature drops, and the output shaft of the drive stops rotating.