# A Pneumatically-Actuated Mouse for Delivering Multimodal Haptic Feedback
## 4 Multimodal Haptic Effects
### High Frequency Vibrations  
High frequency vibrations can be generated by rapidly opening and closing the positive and negative valves alternatively. In order to render synchronous vibrations, the positive and negative valves should be opened for the same amount of time during each cycle. Thus, each valve can be opened for a maximum of half a cycle, and as a result we achieve a duty cycle (the amount of time for which a valve is open) of 50% for each valve. This ensures that all the air that is pumped into the air chamber during the positive valve opening is extracted during the negative valve cycle. The two main characteristics of a vibration signal are its amplitude and frequency. The amplitude (displacement of the stretchable layer) of the vibrations is governed by the amount of time the positive valve remains open during each cycle.  
The frequency of vibrations is calculated by the speed at which the solenoid valves can open and close. The solenoid valves used in the haptic mouse have a response time of 2 ms. In one cycle we operate both the valves for 2 ms; therefore, the total minimum duration required by the valves is 4 ms. The highest frequency that can be achieved with a 4 ms response time is 250 Hz (as \(f=\frac{1}{T}\)). Thus, the highest frequency which can rendered with the haptic mouse is 250 Hz.  
The rendering frequency and duty cycle (while less than 50%) can be changed according to the needs of application. The frequency and duty cycle are sent to the Arduino from a computer and the Arduino calculates the corresponding duration for opening each valve. This is achieved through the following formula.  
\[T=\frac{1000}{f}\omega \tag{2}\]  
where \(f\) is the desired frequency and \(\omega\) represents the desired duty cycle. An example of 250 Hz frequency at 50% duty cycle is provided in Figure 5a.  
Experiment: Relation Between Frequency and Acceleration  
After establishing the maximum possible frequency and duty cycles for the haptic mouse, it is important to calculate the amount of acceleration/displacement that is produced by the haptic mouse at various frequencies and to establish whether the displacements at different frequencies are perceivable.  
Setup and Procedure: In this experiment, a total of nine (1, 2, 5, 10, 25, 50, 100, 125, 250 Hz) different frequencies were rendered at 50% duty cycle. An accelerometer (ADXL335; Analog Devices, Inc) was attached on one side of the haptic mouse which recorded the acceleration. A total of five seconds of data was collected for each frequency at a sampling frequency of 1000 Hz. The acceleration values were collected from the axis perpendicular to surface where accelerometer was attached. The whole experiment was conducted for two different air pressure levels, i.e., 5 and 10 psi.  
Results: Figure 4(b) shows the relationship between frequency and acceleration in gravitational force (g-force or Gs) units. It can be seen that the haptic mouse produces greater acceleration/displacement at lower frequencies. As the frequency increases, the magnitude of acceleration also decreases. This can be accredited to the fact that at lower frequencies the valves remain open for longer duration. A longer opening duration results in a higher change in volume of the haptic mouse and thus creates a higher acceleration value. Furthermore, the haptic mouse produces higher acceleration at 10 psi as compared to 5 psi across all the frequencies due to higher air pressure (more air entering the mouse in the same amount of time).  
The acceleration magnitude achieved for 10 psi air pressure ranged from 0.1 G to 0.6 Gs. According to [31; 32], this range of acceleration magnitude is sufficient and effective for human perception. Therefore, it was decided to use the 10 psi air pressure for vibration feedback.