# A Fiber-Optic Six-Axis Force Sensor Based on a 3-UPU-Compliant Parallel Mechanism
## 1 Introduction  
Six-axis force sensors are widely used in industrial automation, robotics technology, automotive engineering, aerospace and other fields [1]. The elastic body of a force sensor has a significant impact on its performance. According to the different structural forms, the elastic body of a six-axis force sensor can be divided into two types: integral structure and assembled structure. Integrated processing technology is adopted in elastic bodies with integral structure. Cross-beam structure [2] and column structure [3] are two typical structures of an integral elastic body. The advantage of the integral elastic body lies in its good mechanical decoupling performance and small measurement error. However, its measurement accuracy is greatly affected by the processing accuracy of the elastic body, which usually requires precision machining. In the assembled elastic body, modular components are assembled to transmit multidimensional mechanical information. The Stewart structure is one of its typical examples [4]. Compared to the integral elastic body, the component processing of the assembled elastic body is simpler and the cost is lower. The force sensors based on resistance strain [5], piezoelectricity [6] and capacitors [7] are well-developed and widely used nowadays. The force sensors based on resistance strain convert force signals into electrical signals by resistance strain gauges fixed on elasticbodies. And then, each component of force can be obtained by using the force-electric coupling mathematical model [8]. Piezoelectric material (such as quartz) is used as the sensitive element in piezoelectric force sensors. When an external load is applied to the piezoelectric material, the internal charge of the material is changed and an electrical signal proportional to the applied force is generated. By solving the electrical signal, the size and direction of the external load can be obtained [9]. For the force sensors based on capacitors, force signal detection is achieved by detecting changes in capacitance. The capacitor is connected with the elastic body. When an external load is applied to the elastic body, the parameters (such as electrode spacing, effective area and dielectric constant) of the capacitor change, which results in a change in capacitance. By detecting the change in capacitance, external load information can be inferred [10]. However, the types of sensors mentioned above demonstrate the poor resistance to electromagnetic and cross-sensitivity to temperature. Optical fiber sensors offer advantages such as compact size, immunity to electromagnetic interference, corrosion resistance, and high-temperature tolerance, making them more suitable for application in complex environments [11]. Optical fibers have been used to measure parameters such as temperature, pressure, current, displacement, and gas concentration. In recent years, optical fibers have gained attention from researchers and have been increasingly applied in force sensors [12]. A six-axis force sensor based on bending-sensitive optical fibers is proposed in this paper. The bending-sensitive optical fiber is produced by introducing a sensitive region on the fiber surface. It can directly detect the curvature of structure. The authors of this paper have conducted relevant studies on it in previous studies. The operation principles of the bending-sensitive optical fiber are shown in [13]. In [14], the Monte Carlo simulation by ray tracing and an orthogonal matrix are used to optimize the configuration of the sensitive region. This kind of fiber has many advantages, such as high sensitivity, bending direction identification and linear output. It has been used to measure many parameters, such as wind speed, hand joint angle and water waves [15; 16]. In this paper, the parameters of the sensitive region are the same as the optimized configuration in [14]. A 3-UPU-(universal joint-prismatic joint-universal joint) compliant parallel mechanism is designed to accommodate the bending-sensitive optical fibers.