# Design and Experimental Evaluation of an Electrorheological
## 2 Design and Characterization of the Haptic Module
### Design and Working Principle of Miniature ER Actuator  
A prototype ER actuator capable of generating both tactile and kinesthetic sensations was engineered in an earlier study by authors. While detailed design and experimental results of the prototype actuator can be found in the study by [PERSON] (2020), this section intends to recollect the working principle of the ER actuator and its key performance as background information in the context of the current study. Particularly, understanding the dynamic force behaviors of the actuator would be useful for comprehending the experimental results of the actuator with the embedded sensor. Figure 1 illustrates the form factor and working principle of the cylindrical ER actuator. When a user presses upon the membrane surface, the grounded spring electrode is displaced vertically, squeezing the fluid between the grounded spring electrode and high voltage electrode (i.e., squeeze mode, shown in red in Figure 1). Due to the pressure gradient from the press, fluid flows radially outward through parallel electrodes fixed in place (i.e., flow mode, shown in blue in Figure 1). Hence, the actuator operates in both squeeze and flow modes. To compensate for the change in volume due to pressing, the actuator features radial slots allowing the membrane between the slots to deform elastically, forming a reservoir (see Figure 1b). Upon releasing the press, the reservoir lowers, and the actuator returns to its pre-pressed state due to the electrode spring and membrane's elasticity. When a voltage is supplied to the electrodes, the ER fluid's suspensions form fibrous networks parallel to the field lines between the electrodes. This microstructural transformation results in yield stress with a magnitude corresponding to the applied field strength. Therefore, the force felt by the user's finger while pressing is a function of the applied voltage. As the magnitude of the voltage increases, the force required to cause the fluid to flow increases, providing a controllable range of kinesthetic feedback. By introducing a frequency to the applied voltage, the resistive force may fluctuate, resulting in various tactile feedback responses. Thus, the user may feel a dynamic range of simultaneous kinesthetic and tactile sensations. Table 1 presents the actuator's key dimensions and material properties. Notably, the actuator measures only 6 mm thick and 42 mm in diameter, making it relatively small compared to equivalent kinesthetic devices. The gap between the spring electrode and HV electrode is initially 1.3 mm. The actuator may be pressed to a maximum depth of 1 mm, reducing this gap to 0.3 mm. The fixed electrodes are spaced at 1.8 mm apart. The membrane consists of two layers. The contact layer is made of a PDMS film and is adhered to the structure by acrylic tape (3M\({}^{\text{TM}}\) VHB 4910, MN, USA). The actuator's internal volume is filled with 2 mL of giant electrorheological (GER) fluid (Smart Materials Laboratory Ltd., Kowloon, Hong Kong), a type of ER fluid that exhibits a high yield stress nearly an order of magnitude greater than that of conventional ER fluids [59,60]. Figure 2 illustrates the haptic capabilities of the actuator by measuring the force generated over the actuator's indentation under different excitation signals. As shown, the actuator has a maximum indentation depth of 1 mm. Figure 2a presents the actuator's kinesthetic output. As the applied voltage increases, the resistive force increases due to the fluid's increasing yield stress. With no voltage applied, the maximum force posed by the actuator was found to be 2.7 N at maximum depth. The maximum force produced by the actuator was about 6.2 N under a 4 kV load. These forces are sufficiently large to give many distinguishable levels of feedback to users based on the stiffness just-noticeable-difference [61]. Additionally, as shown in Figure 2b, introducing a frequency (i.e., 5 Hz sine wave as shown) to the applied signal results in tunable levels of tactile feedback.