## 1 Introduction  
Touchscreens have become increasingly popular in electronic devices due to their quick and intuitive use. As a means to provide a more engaging and accurate user experience, many touchscreen devices feature vibrotactile feedback. Vibrotactile feedback attempts to emulate physical interactions, such as mechanical buttons, textures, and friction, which are not typically present in touch displays [1]. This is especially beneficial for users that are visually impaired or have other disabilities [2, 3]. Visual displays integrated with vibrotactile feedback have been shown in studies to improve user input speed, accuracy, and satisfaction compared to similar displays without such feedback [4, 5, 6]. Vibrotactile feedback can provide users with a variety of sensations depending on the intended application and on-screen visual feedback. In addition, vibrotactile feedback systems that can provide a variable feedback response strength can be used to convey different types of messages depending on the feedback magnitude. The benefits and applications of vibrotactile feedback are vast, making it highly desirable in many touch display applications. Large touchscreen displays are currently being implemented in a multitude of applications, including automotive dashboards, information kiosks, tablet computers, and touch bars in laptop computers. Despite the many benefits offered by vibrotactile feedback, it is still missing in most large touchscreen displays. Many small mobile devices, such as smartphones and smartwatches, utilize a combination of visual, audible, and tactile feedback to convey information to their users. In order to provide tactile feedback in mobile devices, various vibrotactile actuators (such as eccentric rotary motors, linear resonant actuators, and piezo actuators) have been developed and commercialized [7; 8; 9]. However, this technology is not typically available in large touchscreen devices. This is because most haptic actuators are small and lightweight, being designed primarily for mobile devices. These actuators fail to create adequate vibrotactile feedback when applied to larger screens, often because of an insufficient vibration magnitude or inability to produce feedback throughout the screen. Currently, the technology associated with electrostatics is being studied to provide haptic feedback for large touchscreen applications. [PERSON] and [PERSON] proposed a visuo-haptic feedback system for providing haptic feedback to multi-users on a large touchscreen display using electrostatic haptic feedback and built-in capacitive sensors [10]. The sensation occurs when an electrically charged substance acts on one charged surface and a conductive fluid under the skin acts on the other [11]. Despite their simple structure and scalability for large display applications, electrostatic devices are immature for commercialization. Electrostatic display modules are limited in generating realistic haptic sensations, such as button click sensation, because they provide vibrotactile feedback when the finger slides on the touch surface [12]. Moreover, the performance of electrostatic touchscreens can be considerably affected by environmental factors, such as humidity and temperature [13; 14]. Considering the limitations of existing haptic actuators and electrostatic display technologies, there exists a need to develop a new actuation system capable of generating a freely positionable and fully controllable point of vibrotactile stimulation with satisfying force output at any point in a large touchscreen display. In addition to the need for developing haptic actuators geared toward large touch displays and interfaces, generating haptic sensations across large touch surfaces poses a challenge [15]. Controlling vibrotactile sensations at specific locations, or vibrotactile haptic localization, is being studied for small touchscreen applications [16; 17]. This shows promising potential for use in small displays but is difficult to achieve in large displays.