# Wearable Haptic Device for Stiffness Rendering of Virtual Objects in Augmented Reality
## 3 Experimental Study: Stiffness Rendering of Virtual Objects
### Results  
The experimental results for each feedback condition are presented in Table 1 and plotted in Figure 6. Then, the mean values (and the standard deviations) of perceived stiffness and realness are obtained quantitatively, which clearly shows the effect of each feedback condition. The condition of rigid kinesthetic haptic feedback \(KH_{r}\) is obtained by 4.92, which is the highest corresponding to the object between \(o_{r}=6\) and \(o_{e}=4\). This means that, although the value slightly lacks for rendering perfectly rigid objects, it is still larger than \(o_{e}\) (a rubber ball) or any other feedback, which certifies that the kinesthetic haptic feedback is suitable than any other feedback for rendering fairly stiff objects in the AR environment. Moreover, as shown in the results of realness, the rigid kinesthetic feedback is also the highest value 4.82, and this result verifies that the importance of the kinesthetic haptic feedback in finger-based interaction. The results of the standard deviations, 0.81 and 0.57 (between subjects) for the perceived stiffness and 0.90 and 0.77 (between subjects) for the perceived realness, are also rather small, which implies that the subjects perceive consistently for clear/strong kinesthetic haptic feedback regardless of users. From the results of standard deviation and realness, the efficacy of the proposed passive mechanism for the kinesthetic feedback is also verified. For the condition of elastic kinesthetic haptic feedback \(KH_{e}\), the perceived stiffness is measured by 3.56, which is similar to the stiffness of the object \(o_{e}\). This result means that the kinesthetic haptic feedback generated by a stiff spring can deliver the sense of stiffness of elastic real objects such as rubber, fabric, or skin of a human. Moreover, the realness of the feedback is measured by a fair high value, 4.25, with a small standard deviation 0.84; thus, the elastic haptic feedback can realistically generate the elasticity of virtual objects. These results verify the validity of the proposed selective locking module for elastic kinesthetic feedback, which can be used for rendering elastic/deformable materials (e.g., rubber, fabric, or skin of a human). The stiffness rating of the vibrotactile feedback condition \(VH\) shows a similar stiffness value of 3.16 with that of \(KH_{e}=3.56\) or \(o_{e}=4\). This result implies that the vibrotactile feedback is also effective on a certain level for rendering elasticity similar to the elastic kinesthetic feedback, which again verifies the effectiveness of vibrotactile feedback for virtual object interaction as presented in previous studies [10,18]. However, the standard deviation of the feedback is a rather larger value (1.20 and 1.39) than those of the elastic haptic feedback (0.97 and 1.34), which means that the rendered stiffness from \(VH\) is inconsistent for each trial or each user. The realness metric is also relatively smaller 3.37 compared to the elastic kinesthetic feedback conditions (4.82 and 4.25). This result indicates that the realness can be substantially increased from no feedback condition, which is also consistent with VR results (increased presence or task-performance by using the vibrotactile feedback [29]), yet a limitation of the vibrotactile feedback in AR that is solely utilizing the feedback lacks a vivid illusion of stiffness. In case of the condition for the pseudo-haptic feedback \(PH\), the stiffness value 1.45 is fairly smaller than the other haptic feedbacks or even the soft real object \(o_{s}=2\), which shows that the adopted visuo-haptic feedback is not suitable for rendering stiff virtual objects. However, the result of realness has a much higher value 4.28 than no feedback