# A Pneumatically-Actuated Mouse for Delivering Multimodal Haptic Feedback
## 4 Multimodal Haptic Effects
### Static Pressure  
Static pressure can be defined as a certain amount of pressure or force exerted over a sustained period of time. In the current system, static pressure is achieved by opening the positive valve for a given duration of time and then closing it (while also keeping the negative valve closed). The volume of the air chamber grows as long as air is blown into it (while remaining below the mechanical tear point). When the valves are closed, the air remains trapped inside the chambers and thus produces  
Figure 3: Pneumatic controlled hardware system showing all the components used in the control module.  
the sensation of static pressure on the hand holding the haptic mouse. Once the static pressure is no longer required, the negative valve is opened and the trapped air is allowed to escape, bringing the haptic mouse to it's initial state.  
The main variable in producing static pressure is the duration of time for which the positive valve is opened. The amount of static pressure can be adjusted by operating the valves. It can be increased by reopening the positive valve, or decreased by opening the negative valve for a certain amount of time. An example is given in Figure 3(a), showing static pressure for having an initial opening duration of 150 ms and a subsequent one of 75 ms.  
Experiment: Relation Between Volume and Duration  
The key factor in rendering and perceiving static pressure is the amount of increase in the volume of the haptic mouse. In order to render a given volume successfully, the relationship between volume and duration of opening the valves should be calculated. For this purpose, an experiment was carried out to map the duration of opening of valves against changes in volume at different air pressure levels.  
Setup and Procedure: In this experiment, the maximum duration for opening the positive valve was fixed at 880 ms, in order to avoid damage to the air chamber. The positive valve was opened in increments of 40 ms at a time, so as to achieve a continuous relationship between duration and volume over the course of 880 ms (22 increments). The volume calculation includes the length, width, and height; however, in our current case, the length dimension of haptic mouse was constrained. Thus, change in volume occurred only through changes in width and height.  
Figure 4: Quantitative analysis of static pressure rendering by haptic mouse.  
The default width of the haptic mouse was 36 mm and height was 42 mm, while length was 24 mm and kept constant.  
The whole experiment was carried out at two different air pressure levels, i.e., 5 and 10 Psi. Each experiment was repeated three times and the results were averaged.  
Results: Width and height changes were individually calculated for the increasing duration. As mentioned earlier, length of the mouse was kept constant by clamping it and stopping it from expanding. The shape of the haptic mouse can be considered as one half of an ellipsoid. The formula for calculating the area of an ellipsoid is,  
\[volume=\frac{1}{2}\cdot\frac{4}{3}\pi\alpha\beta\gamma \tag{1}\]  
where \(\alpha\), \(\beta\), and \(\gamma\) are the length, width, and height of the ellipsoid. The \(\frac{1}{2}\) was used because the haptic mouse was half an ellipsoid. The changes in width, height, and volume with respect to duration are given in Figure 4.  
As is evident, an increase in duration resulted in an increase in the total volume of the haptic mouse. Initially, increase in duration of air flow caused a rapid increase in volume; however, after some time the increase in volume slowed down, and towards the end, i.e., above 800 ms, an increase in duration caused only a negligible increase in volume. The air had higher pressure at 10 psi as compared to 5 psi, and thus the total volume increase at 10 psi was higher than the volume increase at 5 psi.