## 1 Introduction
ERM actuators also produce relatively weak vibrations due to the small size of the mass. Increasing the size of the mass would increase the vibration strength but would also accentuate the actuator's weaknesses, making it not a feasible option for vibrotactile haptic use [11]. Linear resonant actuators (LRA) use an electromagnet and spring mechanism to provide vibrotactile sensations. These devices are small and have a faster startup time (about 20 ms) compared to the ERM actuator, but they also produce a lot of residual vibrations and are limited in to use at their resonant frequency [10; 11]. These actuators also cannot create sufficiently large vibration forces for large touchscreen applications. A specialized linear impact resonant actuator was developed by [PERSON] et al. that could be used at a wide range of frequencies with low power consumption, but it could only generate a maximum of 3 g-forces at the resonant frequency [10]. This could be applied to mobile touchscreen applications but is still not sufficient for use in larger screens. Increasing the size of an LRA would increase the response time and greatly increase power consumption, limiting its use in large touchscreen applications [11]. Piezoelectric or piezo actuators can create a wide variety of precise tactile sensations due to their short startup time (as little as 5 ms) and their possibility to create short-duration vibrations (under 3 milliseconds) [10]. They also operate at a wide range of frequencies, altogether creating high-fidelity sensations. Piezo actuators can create almost any kind of one-dimensional haptic sensation with a relatively large dynamical range. However, they also create a potentially unwanted sound when actuating, whose frequency and volume depend on the material, environmental, and driving factors [12]. Piezo actuators are very thin, which can be ideal for use in electronic devices but also makes them very fragile. Although piezo actuators could be attached to touchscreen panels to cause direct vibration, this is not desirable because of reliability and durability issues [11]. These actuators being expensive and requiring a lot of operation power, along with the previously mentioned disadvantages, make them not ideal for large touchscreen applications. Electrostatic actuators rely on electrostatic attraction forces to create haptic sensations. Typically, parallel plate actuation is employed in electrostatic actuators where one electrode is fixed and another is moveable via a spring, causing oscillations. The electrostatic attraction force directly depends on the electrode area, making it easy to scale up in size. Furthermore, the small distances involved can create large electrostatic fields. One important disadvantage of parallel plate actuators is the concept of snap-in. The spring restoring force is linear, while the electrostatic attraction force is not. This limits the displacement range of the electrode to about one-third of the original gap [13]. Electrostatic actuators are often used in haptic applications that benefit from a small and flat module, which could be as little as a few microns [14]. The easy scalability of the plates allows electrostatic actuators to be made specifically for large touchscreen applications. Frequency beating can be used in electrostatic actuators to simultaneously activate multiple mechanoreceptors on the skin which creates a multitude of unique sensations. An electrostatic beating actuator with no mechanical vibrotactile actuators was presented and characterized in a study by [PERSON] et al. [15]. This study exemplifies one of the many ways electrostatic actuators can be utilized. However, these devices typically still cannot create sufficiently large vibration sensations when mounted onto a touchscreen. Recently, [PERSON] et al. studied a new electrostatic actuator, or electrostatic resonant actuator (ERA), for large touchscreen applications.