# Flexible Shear and Normal Force Sensor Using only One Layer of Polyvinylidene Fluoride Film
## 1 Introduction  
In recent years, the importance of flexible tactile sensors has increased owing to the development of wearable electronics and intelligent robots [1; 2; 3]. In the same context, various studies have been performed to enable these flexible tactile sensors to sense external inputs such as proximity [4; 5], strain [6; 7], and pressure [8; 9]. Among these sensors, force sensors have been widely used in the field of robotics to realize functions such as object classification [10] and robot manipulation with a feedback system [11; 12]. During the time of force sensing, it is very important to detect shear force as well as normal force. This is because, in reality, most of the force is applied in combination with the normal direction and the shear direction.  
Force sensors that can sense shear and normal forces have been broadly studied. These sensors typically utilize the capacitive [13; 14; 15], piezo-resistive [16; 17; 18], and piezoelectric [19; 20; 21] properties of materials. Of these sensors, the capacitive ones have excellent sensitivity, large dynamic range, and good spatial resolution. The piezo-resistive ones have a high spatial resolution and a simple construction. Both of them require bias voltage, which consumes electric power.  
In contrast, the piezoelectric ones have the characteristic advantage of being self-powered, i.e., they generate electrical signals under external mechanical inputs [22; 23]. With this benefit, several studies have been performed with piezoelectric force sensors that can measure shear forces [24; 20; 21; 25; 26]. Specifically, therein, some researchers have assembled polydimethylsiloxane (PDMS) bump structures on flat or micropillar-type polyvinylidene fluoride (PVDF) and have used electrodes of specific shapes for effective sensing, resulting in the detection of shear and normal forces. These fabrication methods are, however, complicated to perform owing to processes such as lithography and sputtering.  
In this paper, we proposed a force sensor that could be fabricated through a simple process using only one layer of PVDF film and PDMS, and that could measure not only normal force but also shear force. Since the spatial resolution of the force sensor is required for applications in robotics [1], the sensorsare fabricated into arrays to demonstrate their practical applicability. In general, PVDF has been used as a sensing material because of its flexibility, biocompatibility, and good performance [27; 28; 29; 30; 31; 32; 33; 34; 35]. In addition, the PVDF generates internal electric potentials through mechanical deformation, so we can sense the force using this measured electric signal. The top and bottom PDMS of a 3D trapezoid structure seals one layer of PVDF film, enabling it to sense shear and normal forces. Herein, the PDMS acts as an insulator so that the sensor is not affected by an external electrostatic field. The sensing capability of the sensor was investigated by applying different forces in different directions, and then the direction and magnitude of the applied forces were estimated. Furthermore, when the forces were applied, the morphology of the PVDF film composed of one domain was investigated by using the finite element method (FEM) procedure in the COMSOL Multiphysics software. Finally, we have presented a real-time measurement system for practical applications of the sensor array. Therein, the sensing system can display the magnitude and direction of the unknown force applied to the sensor in real time.