# Wearable Haptic Device for Stiffness Rendering of Virtual Objects in Augmented Reality
## 3 Experimental Study: Stiffness Rendering of Virtual Objects
### Procedures
#### 3.2.2 Stiffness Discrimination Phase  
After the referencing phase, we perform a trial that consists of a grasp task and an answer task. The procedures of the grasp task of each trial are shown in Figure 5B (middle), where a virtual sphere is displayed on the surface of the table plane, and their position is randomly determined within the predefined range from the center of the plane (rectangular area of 20 cm width and 10 cm height). The size of the sphere is fixed to 4 cm, which is the same as the previous real objects in the referencing phase. The subjects can sense the stiffness of the sphere by two-finger for five seconds. The type of feedback for the subjects is also randomly selected among the mentioned conditions for each trial.  
After the grasp task, the subjects are asked to answer two multiple-choice questions as shown in Figure 5B (right). The GUI panel, where the subjects can answer their responses by pointing gestures, is displayed in AR, which is same with the referencing phase. The first question asks the subjects to represent the perceived stiffness from the grasping task, compared with the real objects in the previous referencing phase. Thereby, there are seven  
Figure 5: (**A**) The sensing box for the sensing referencing phase, which includes three real objects with different stiffness; rigid stiffness \(o_{r}\) (a plastic ball), elastic stiffness \(o_{e}\) (a rubber ball), and soft stiffness \(o_{s}\) (a sponge ball); (**B**) experimental procedure: the subjects sense the stiffness of the real objects through the sensing box (**stiffness referencing phase**), and are asked for two-point grasping for the displayed virtual object and then answer the realness and stiffness of the object compared with the real objects to the GUI AR panel (**stiffness discrimination phase**).  
levels of choices; over the object \(o_{r}\), similar to the object \(o_{r}\), between object \(o_{r}\) and \(o_{e}\), similar to the object \(o_{e}\), between object \(o_{e}\) and \(o_{s}\), similar to the object \(o_{s}\), below the object \(o_{s}\). For example, if a subject senses the presented virtual object as hard as \(o_{e}\), the subject rates the stiffness by level four as shown in Figure 5A.  
The second question asks the subjects about the realness of the virtual sphere, which is one of the most important factors implementing virtual objects [36]. Thereby, we ask the users \"Was touching the virtual object just as natural as touching the real object?\", which is a modified version of the question about realness in [36], and the answer is rated on a seven-point Likert type scale. Thus, the subjects are instructed to rate level seven when they feel a virtual object as a real object in the grasping task, or rate level one when they feel like touching a perfectly virtual object. The subjects answer the questions on the panel in AR immediately after each trial.  
The number of trials is 50 times, which has a duration of about fifteen minutes for each subject. In addition, the subjects are instructed to perform the stiffness sensing phase in every 10 trials, to recall the sense of the stiffness of the real objects. A total of eight subjects participate in the experiments. The subjects are all right-handed males in the age range of 22 to 31 years, with no known perception disorders. The experiments are conducted in accordance with the requirements of the Helsinki Declaration. The overall procedures of the experiment are described in the supplementary videos.