**1. Introduction**

Tactile feedback technology reproduces the tactile sensation for the user through a force, vibration, or other excitation methods [1]. Touch might be the most complex sensing modality compared to sight, hearing, smell, and taste [2]. The technology can be applied to assist the creation and control of virtual scenes and enhance the remote control of machinery and equipment. Tactile feedback technology is usually applied to tactile displays, or touch sensors and other equipment [3]. Some devices are able to reproduce the tactile of the textured surfaces under the finger [4,5]. Tactile feedback technology has been successfully applied in virtual reality gloves, virtual medical, tactile display, and other fields [6]. According to the excitation method, the tactile feedback device can be classified into a pneumatic type, an electromagnetic type, and a piezoelectric type. Among them, the tactile feedback device using piezoelectric materials has received wide attention and application. Piezoelectric tactile feedback devices have stable vibration, slow adaptability to vibration, and low stimulation, etc. [7–9]. Additionally, the response time of piezoelectric materials is relatively short, which is suitable for long-term tactile simulation [10].

The first category uses an ultrasonic vibration of piezoelectric material to modulate the contact effect between a user's fingertip and a vibrating surface [11]. For example, Ma Lu et al. designed a tactile reproduction system based on friction control, which realizes tactile shape reproduction by controlling the frequency of the finger in di fferent positions on the tactile plane [12]. It can be explained either by the squeeze e ffect or by intermittent contact of the vibrating surface with the finger [13,14]. Other reports focus on tactile displays realized with stimulator arrays, in which mechanical vibrations are generated to stimulate the mechanoreceptors of the skin. For example, in 2002, Yasushi proposed a TextureExplorer that combines tactile and force stimulators to present virtual textures to the user's fingertip. This provided a vibration pin-array excited by piezoelectric plates employed for tactile stimulation in conjunction with the PHANToM, which is a device for force reflection to perform haptic texture rendering [15]. Hayward from McGill University presented a tactile feedback device based on the principle of piezoelectric lateral skin stretching, which was constructed from an array of 64 closely packed piezoelectric actuators connected to a membrane. The deformations of this membrane cause an array of 112 skin contactors to create programmable lateral stress fields in the skin of the finger pad [16].

Tactile feedback devices based on friction control mostly use a combination of sensors and actuators. The virtual touch is realized by detecting the spatial position of the finger to generate a vibration stimulus or to electrostatically stimulate the skin. However, due to a single stimulation method, the e ffect of tactile stimulation is not optimistic. The tactile e ffect is relatively simple, and the control system is generally more complicated. The tactile feedback techniques based on stimulator arrays can perform haptic texture rendering, but the resolution is related to the number of used actuators. Therefore, the application of a large number of piezoelectric actuators leads to manufacturing di fficulties and high manufacturing costs [17].

To solve the above problems and take advantage of these two technologies, here, we arrange the array tooth structure on ultrasonically vibrating piezoelectric beams, which we call the ciliary body piezoelectric beam. The beam can be any material with elastic properties. So, in this paper, a piezoelectric tactile feedback device with a ciliary body structure is proposed, which has the features of a simple structure and control system. This technique can achieve di fferent touch sensations depending on the direction of finger movement at the same contact position [18]. Firstly, the principle of the anisotropic vibration of the ciliary body structure is analyzed, and a tactile model of the sliding vibration of the anisotropic vibration is established. Secondly, the equivalent friction coe fficient of the skin and the touch beam under full-coverage and local-coverage are deduced and solved. The change law of the equivalent friction coe fficient is analyzed according to the solution results. Finally, the important parameters, such as the proportion of ciliary bodies in the same direction and ciliary bodies' density, are changed. The equivalent friction coe fficient function is solved. The e ffect of each parameter on the friction coe fficient is analyzed, and the tactile control law and scheme are obtained.
