# Precision Calibration and Linearity Assessment of Thin Film Force-Sensing Resistors
## 1 Introduction  
Force-sensing resistor (FSR) sensors are widely used in various applications because of their ability to measure force, pressure, and touch [1; 2; 3; 4]. They play a critical role in fields such as robotics, medical devices, wearable technology, and Human-Machine Interactions (HMI) [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21]. For instance, in robotics, FSR sensors can be attached to robot fingers or feet to detect the weight of objects or the contact force [5; 6; 7; 8; 9; 10; 11; 12]. In medical devices, they can monitor the physiological data of patients and track force changes during rehabilitation training to analyze therapeutic effects or hospitalization periods to prevent pressure scores [8; 10; 11; 13; 14; 15; 16; 17]. In wearable technology, FSR sensors are applied to smart shoes or gloves to collect user activity data and provide personalized feedback [18; 19]. Additionally, in the HMI field, FSR sensors are used in touchscreens or buttons to detect user input and improve the responsiveness of interfaces [12; 14; 15; 16; 20; 21]. Research related to FSR sensors primarily focuses on improving sensor performance, developing new applications, and enhancing data processing techniques [21; 22; 23; 24; 25]. Thin film FSR sensors consist of two thin films with a pressure-sensitive material sandwiched between them. These sensors measure force based on the principle that the contact area between the films increases when force is applied, leading to a decrease in resistance [1; 22; 22]. This characteristic endows thin film FSR sensors with several advantages. First, they have a simple structure and are cost-effective to produce. Second, they are extremely thin and flexible, making them easy to attach to various surfaces. Third, they havea fast response time, allowing for real-time force measurement. Fourth, they can be manufactured in various sizes and shapes, enabling custom designs for specific applications. Despite their advantages, FSR sensors have some drawbacks in terms of linearity, reliability, and accuracy. First, FSR sensors exhibit nonlinear output characteristics, making accurate force measurement challenging. Second, the repeatability and long-term stability of the sensors can be low, leading to inconsistent results under the same conditions during repeated measurements. These drawbacks are significant factors in evaluating and improving the performance of FSR sensors. There have been various attempts to address this problem using different methods [1,2,22]. [PERSON] et al. [23] introduce a technique for conditioning and calibrating force-sensing resistors to ensure repeatable and reliable measurement of compressive force, highlighting its application in ergonomics and rehabilitation. [PERSON] et al. [24] analyze the creep response and dynamic loading behaviors of conductive polymer composites in FSRs, highlighting their long-term stability and performance under varying forces. Their study underscores the potential for enhanced durability and accuracy of FSRs. [PERSON] et al. [25] introduce an apparatus for the static and dynamic calibration of FlexiForce sensors, ensuring accurate force measurements in various conditions and improving sensor reliability and precision. [PERSON] et al. [26] present methods to mitigate errors in force-sensing resistors by using a modified astable 555 oscillator circuit, improving sensor performance through self-compensation. [PERSON] et al. [27] evaluate the use of force-sensing resistors to measure interface pressures in lower limb prosthetics, emphasizing their effectiveness in optimizing prosthetic fit and comfort. In this study, we aim to measure and analyze the output characteristics of FSR sensors using a voltage divider circuit and multiple fixed resistances. Our goal is to determine the suitability of FSR sensors for accurate pressure measurement under different loading conditions.