# A Tiny Haptic Knob Based on Magnetorheological Fluids
## 2 Design of Proposed Haptic Knob
### Design of Rotary Shaft and Housing  
The housing has a hollowed groove for the solenoid coil to fit in, as shown in Figure 2a. It has long and thin grooves on its surface and a pivot for aligning the rotational axis and guiding the rotation of the shaft, as shown in Figure 2b. The rotary shaft was designed to be tightly inserted into the housing; a constant gap was also maintained between the housing and rotary shaft. The MR fluid completely filled the gap to generate resistive torque feedback. Figure 2c shows the cross-sectional view of the housing equipped with the solenoid coil, rotary shaft, and housing cover. We drilled a hole in the rotary shaft to place it into the pivot of the housing (Figure 2d). The rotation of the shaft causes the MR fluids in the gap to move. We included long and slender bumps on the inner surfaces of the rotary shaft to accelerate the flow of MR fluids (Figure 2e).  
There are inclined surfaces in the housing, with oblique angles defined as \(\theta\). The larger the oblique angle (\(\theta\)) of the inclined surface, the larger the total area of the gaps. Therefore, the oblique angle affects the haptic performance (torque feedback) of the proposed haptic knob. To find the optimal oblique angle, we simulated the resistive torque with changes to the oblique angle. Figure 3a shows the simulation result of the resistive torque generated from the proposed haptic knob. It can be seen that the resistive torque increased as the angle of the inclined surface increased. Although an oblique angle of about \(90^{\circ}\) increases the haptic performance of the proposed haptic knob, it is difficult to make a sharply carved shape (@ in Figure 2b). The result also shows that the resistive torque does not significantly increase when the oblique angle of the housing exceeds \(80^{\circ}\). Therefore, we selected an oblique angle of \(80^{\circ}\).  
The gap thickness (g\({}_{\text{I}}\)) (Figure 2c) between the housing and the rotary shaft is an important factor for maximizing the performance of the proposed haptic knob. For this reason, it is necessary to investigate the resistive torque of the haptic knob as a function of the gap thickness at a fixed oblique angle of \(80^{\circ}\). Figure 3b shows the simulated resistive torque of the haptic knob according to the gap thickness without (black line, initial state) and with applied current (red line, operating state). As the gap thickness decreased, the resistive torque of the proposed haptic knob became stronger. The results show that the resistive torque decreased sharply with increasing gap thickness. The ideal haptic knob should have no resistive torque when there is no input current. When the gap thickness  
Figure 1: Schematic and cross-sectional illustrations of the proposed haptic knob: (**a–c**) assembling procedure of the proposed haptic knob; (**d**) assembled haptic knob; (**e**) its cross-sectional view, and (**f**) schematic illustration of the proposed haptic knob when it rotatesexceeds 0.12 mm, the resistive torque in its initial state (without current) is small enough and is almost unchanged, and the operating resistive torque in its operating state (with a current of 250 mA) is sufficient to create a variety of haptic sensations. Therefore, we set the gap thickness to 0.12 mm.  
Figure 3: Simulated resistive torques as a function of the (**a**) oblique angle of the inclined surface and (**b**) gap thickness.  
Figure 2: Detailed structure of the housing and the rotary shaft, and the combined process with the solenoid coil: (**a**) Process for combining the housing and the solenoid coil; (**b**) process for combining the rotary shaft and the housing; (**c**) cross-sectional view of the housing equipped with the solenoid coil, rotary shaft, and housing cover; (**d**) bottom view of the rotary shaft; (**e**) long and slender bumps on the surface of the rotary shaft.