## 1 Introduction  
The flexible lower limb exoskeleton is a mechanical device that can provide strength assistance to the wearer in walking, running, bearing, carrying, and other sports by sharing the load of the hip joint and knee joint. The use of an exoskeleton can reduce the metabolic consumption generated by exercise and improve the human body's long-term exercise ability. In recent years, the application of flexible wearable exoskeletons has made a series of breakthroughs in the military, health care service, transportation, and other aspects of human life [1, 2, 3]. The power-assisted types of flexible exoskeletons can be divided into pneumatic muscle assist and flexible material assist. Pneumatic muscle assist has the characteristics of high efficiency, density, light weight, and flexibility, but it is difficult to have high control accuracy due to its high nonlinearity. In flexible material assist systems, Bowden cable is commonly used to function as the transmission mechanism. The Bowden cable transmission mode operates by transferring the tension and position through the motor contract line distance. Bowden cable transmission has the advantages of small size, remote transmission, and better position control accuracy of the motor, which has become increasingly used in flexible exoskeleton design [4]. The following are some applications of Bowden cable drive in flexible exoskeletons: [PERSON] [5] proposed a novel Remote Execution System (RAS) based on Bowden cables, featuring a high power-to-mass ratio, power-to-volume ratio, simple components, and a compact mechanical design, with waterproof, dustproof, and hygienic characteristics. [PERSON] [6] designed equipment consisting of four motor-driven cable-driven actuators to assist four joint movements. The unique feature of this equipment is the crossover of cables in the front and rear, along with the introduction of the concept of crossover cable assistance. After testing, this device is capable of generating motion in six directions around user joints, including internal and external rotation. [PERSON] [7] developed an autonomous powered leg exoskeleton, which, compared to not wearing the device, reduces walking metabolic costs by 6% to 11%. [PERSON] [8] employed cable-driven and series elastic actuators to design a flexible lower limb assistive exoskeleton, providing support for the elderly and individuals with lower limb disabilities when navigating stairs. [PERSON] [9] devised a cable-driven hip-joint-powered assistive exoskeleton system that significantly reduces muscle consumption during walking, offering effective assistance in human locomotion. [PERSON] [10] developed an exoskeleton utilizing cable-driven knee braces that synergistically assist both the knee and hip joints. The assistive force directly acts on hip flexion and knee extension, while also indirectly impacting hip extension. Additionally, a Parameter Optimization Iterative Learning Control (POILC) method was introduced to minimize errors caused by differences in wearing positions and wearers' biological characteristics. Metabolic reductions of 9.86%, 12.48%, and 22.08% were observed when compared to situations without wearing the soft exoskeleton. In summary, Bowden cable drive has been widely used in flexible exoskeletons, providing effective force assistance and reducing human consumption by combining sensors and control algorithms. However, the key challenge of Bowden cable transmission is how to achieve accurate force control and flexibility. In the Bowden cable system, there is friction between the external hollow wire sheath and the internal wire rope, which makes the Bowden cable system often have tension attenuation at the beginning, and it will cause the attenuation of the output tension too. Therefore, it is necessary to analyze and model the Bowden cable force transmission, so as to accurately control the assisting process.