# A Haptic Feedback Actuator Suitable for the Soft Wearable Device
## 2 Design of Electro-Hydraulic Haptic Feedback Actuator  
As shown in Figure 1, the parts of the electro-hydraulic haptic feedback actuator, from top to bottom, are circular polydimethylsiloxane (PDMS) films, annular electrodes, insulating liquid dielectrics, annular PDMS films, circular dielectric films, annular electrodes, and circular PDMS films. Three layers of PDMS films form a piece of flat, thin, and hollow tablet filled with a type of insulating liquid dielectric. Inside the tablet, a pair of flexible but not stretchable annular electrodes are glued with the upper and lower PDMS films, respectively. Therefore, the two electrodes inside the actuator are insulated from each other by the liquid dielectric and the dielectric film.  
Figure 1: The composition of the electro-hydraulic haptic feedback actuator.  
Figure 2a-d show the action principle of the actuator. When the voltage is applied, the Maxwell force occurs between the two annular electrodes. Then, the internal insulating liquid dielectric in the annular area is squeezed into the center area. The underlying dielectric film restricts the downward flow of the insulating liquid dielectric, and the center part of the upper PDMS film bulges. The annular electrodes provide space for the internal insulating liquid dielectric to flow, and it realizes displacement and force output as a tactile feedback area. The in-situ structure of the electro-hydraulic actuator eliminates the long flow channels of traditional fluid actuators, and the resistance loss is reduced during the actuation process. In addition, the insulating liquid in the cavity can serve not only as a medium for pressure transmission but also as an insulating medium to isolate the two annular electrodes. Therefore, the liquid dielectric can increase the breakdown voltage threshold of the actuator.  
To analyze the relationship between the Maxwell force and the output of the actuator qualitatively, some parameters were derived as follows. When the two electrodes are energized, the Maxwell electric field force between them can be expressed by the following formula:  
\[F_{\varepsilon}=\frac{1}{2}\varepsilon A(\frac{V}{h})^{2} \tag{1}\]  
where \(\varepsilon\) is the absolute permittivity of the actuator, \(A\) is the area of the annular electrode, \(V\) is the applied voltage, and \(h\) is the thickness of the inner chamber.  
Considering the incompressibility of the liquid dielectric, the volume of the actuator should be invariable before and after applying a voltage. The thickness variation can be approximately calculated as  
\[\Delta h=\frac{\pi\cdot H^{3}}{6D_{0}}+\frac{\pi\cdot D^{2}\cdot H}{8D_{0}} \tag{2}\]  
where \(H\) is the arched height, \(D\) is the inner diameter of the annular electrode, and \(D_{0}\) is the diameter of the inner chamber, as shown in Figure 2.  
The driving characteristics of the actuator are affected by the Maxwell force. Equation (1) indicates that the Maxwell force is related to the voltage applied on the two electrodes, distance, and relative area between the electrodes. To increase the Maxwell force, the two electrodes are placed inside the dielectric films to reduce the distance between them, as shown in Figure 1. In addition, the relative  
Figure 2: Schematic diagram of the electro-hydraulic haptic feedback actuator with (**a**) Voltage OFF and (**c**) Voltage ON. (**b**) The action principle of the actuator. (**d**) Cross section of the actuator before and after power on.  
area between the electrodes should be enlarged as much as possible. However, this area contradicts a compact design. After several tests, the key structural parameters of the actuator were determined to gain a good haptic feedback effect, and the parameters are described in the Experimental section.