## 4 Overview of Wearable Interface for Providing Haptic Feedback
Indeed, recent scientific works revealed much interest in creating mid-air tactile feedback devices based on ultrasound; these latter ones enable the induction of tactile sensations at any place and time without hindering human mobility. In the literature, several works were presented that exploit  
Figure 10: Three-dimensional model of the presented ungrounded tactile device with the main components highlighted (**a**) and the assembled device without the handle (**b**) [69]. the abovementioned effects employing transducers' arrays, which were brittle, heavy, and stiff. [74; 75]. In their work, [PERSON] et al. introduced a novel tactile interface relying on printed polymer transducers (PPTs). They also focused on developing PPTs piezomembranes deposited using a printing process. The membrane is a sandwich of polyimide (substrate) and P(VDF-TrFE); the element connections were realized using metallic electrodes, and the element edges were formed by a thick organic material. The PPTs are fully flexible, given their reduced thickness (<0.25 mm) and weight, making them suitable for wearable applications [76]. Tests indicated that a 2 mm displacement was obtained for PPT stimulated at its primary resonance of 29.5 kHz with a 500 V amplitude [77]. One of the most widely used haptic feedback strategies to provide users with tactile information is vibrotactile feedback. High-frequency stimuli are produced by a vibrotactile actuator and trigger FA-type mechano-receptors [78; 79]. Numerous tactile interfaces necessitate a substantially wider contact area [56; 57], such as the torso or waist, because such mechanoreceptors have larger receptive fields [80; 81; 82]. As a result, several tactile interfaces have been created to deliver relatively basic alerts or give the user geographic location data for navigating. Nevertheless, finding a haptic system where a person can use their hand to engage with a virtual world by sensing local touch represented by vibrotactile feedback is challenging. Despite vibrotactile feedback's benefits, such as rapid user reaction times, it is usually used for applications requiring a greater contact area. A first example is the following study by [PERSON] et al., which presents a vibrotactile-array type tactile interface applied to the fingertip for VR/AR applications [83] (Figure 11). A previous study by the same authors showed that a participant could recognize a virtual item's 2.5D shape produced with a finger-tip haptic interface that used a two-by-two tactile matrix (Figure 11a) [84]. Then, the authors upgrade their system by extending haptic contact with three-dimensional objects. A fingertip image is translated to the fingertip location using the hand's position data [83]. In a different study, the same researchers presented two finger-tip interfaces for the index and thumb fingers. The type-A interface was originally intended to generate 2.5D surface characteristics [85]. It contains four fingertip-sized piezoelectric actuators, each consisting of a ceramic disk with a 9 mm diameter placed coaxially on a metal plate with a 12 mm diameter. The second typology of vibrotactile fingers haptic interface (type B) is depicted in Figure 11b. Figure 11: Three-dimensional model and screenshots of type-A (**a**) and type-B (**b**) tactile interfaces applied on fingertips. LF, LR, RF, and RR stand for the locations of the piezo actuator [83]. Continuous motion is another prerequisite for a realistic representation of a contact point. By carefully determining the elapsed time between the onsets of successive actuation, [PERSON] and [PERSON] proved that discontinuous vibrotactile arrays could give the impression of continuous motion [86; 87]. The duration is further known as inter-stimulus signal onset asynchrony (SOA). The following criteria must be met to produce the perceived tactile movement:  
\[\text{SOA}=0.32\cdot\text{Ts}+0.0473 \tag{4}\]  
where Ts and SOA are the temporal distance between consecutive actuation's onsets, respectively.