# Wearable Haptic Device for Stiffness Rendering of Virtual Objects in Augmented Reality
## 2 Wearable Haptic Device for Stiffness Rendering in AR
### Tendon Locking Part  
The main component of the proposed haptic device is the tendon locking part, the structure of which is shown in Figure 2A and the supplementary videos. The plate of each finger is connected with the locking part by the tendon. The tendon is fixed on a wall of the part, sequentially connected with a soft spring (\(k_{s}\simeq 100\) N/m) which generates free tension to prevent slack in free hand motion, and a much stiffer spring (\(k_{c}\simeq 2000\) N/m) which renders stiffness of elastic objects. Moreover, the tendon-spring is wound to two pulleys (an elastic mode pulley and a rigid mode pulley), where the braking force from the above servo motor is exerted. The bearings are located on the axes of the pulley to  
Figure 3: The structure and components of the tension transmission part (**A**) and those of the actuator fastening part: the hook and velcro band are on the outer side (**B**), and the frictional polymer is on the inner side of the glove (**C**).  
Figure 2: (**A**) Structure and components of tendon locking part, and the mechanism of each stiffness mode; (**B**) free motion mode (**C**) elastic mode, and (**D**) rigid mode. Along with the configuration between the arm/pawls and pulleys (**B1,C1,D1**), the breaking point (red) and effective stiffness of the tendon-spring (green) are also changed (**B2,C2,D2**).  
decrease friction in free motion. In the housing of the locking part, the placement of the tendon-spring is optimized to cover maximal displacement of the springs from finger motions (about 2 cm in a pilot test) while minimizing the size of the component.  
The proposed device can render two types of stiffness corresponding to rigid/elastic objects by altering the effective stiffness of the tendon-spring structure via a selective locking of one of the pulleys. A servo motor is placed above the tendon-spring and pulleys, which has an arm to break the pulleys when actuated. To maximize the braking force, the upper side of the pulleys and the arm of the motor takes forms of gear and pawl, respectively.  
Descriptive figures of the mechanism are shown in Figure 2B,C. In the free motion mode (Figure 2(B1,B2)), the configuration of the arm is horizontal, thus the pulleys can freely rotate, which leads to smooth free motion and slack prevention. In the elastic mode (Figure 2(C1,C2)), the servo motor is rotated in a counter-clockwise direction and the left pawl fixes the elastic mode pulley. Then, only the stiff spring is connected with the tendon so the user can feel the haptic sensation of elasticity when touching virtual objects. In the rigid mode (Figure 2(D1,D2)), the servo motor is rotated in a clockwise direction and the right pawl fixes the rigid mode pulley. Then, no spring is connected with the tendon so the user can sense the illusion of touching a rigid object while preventing the interpenetration of the finger-tip simultaneously. In summary, the effective spring constant of the tendon-spring structure can be expressed in the following form:  
\[k_{eff}=\begin{cases}\frac{k_{e}k_{e}}{k_{e}+k_{s}}\simeq k_{s}&\text{free motion mode}\\ k_{e}&\text{elastic mode}\\ k_{tendon}\gg k_{e}&\text{rigid mode}\end{cases} \tag{1}\]