# Kinematic Analysis and Motion Planning of Cable-Driven Rehabilitation Robots
## 1 Introduction  
With the number of patients with limb injuries caused by unknown diseases or unexpected accidents increasing year by year [1; 2], scientific and effective rehabilitation therapy plays a significant role in restoring limb motor function. In the early stage of rehabilitation, meaningful and repetitive rehabilitation training tasks can help patients with motor dysfunction improve their muscle strength and coordination [3; 4]. Traditional rehabilitation treatment requires rehabilitation training under the guidance of rehabilitation specialists. Due to long-term training, the rehabilitation teacher's strength is weakened and the movement is biased, which leads to a weakening of the rehabilitation effect. For repetitive rehabilitation treatment, rehabilitation robots can be used instead of rehabilitation specialists [5]. Therefore, rehabilitation robots have received great attention. Some exoskeleton rehabilitation robots have been widely applied in rehabilitation treatment, and help patients complete rehabilitation training more effectively through auxiliary training and real-time status monitoring [6], such as ARMin [7], RUPERT [8], and CADEN-7 [9]. However, the traditional exoskeleton robot has large inertia, and the patient is prone to collide with the robot, causing secondary injury to the patient. There are problems such as limited working space and a single training mode [10; 11; 12]. For these reasons, in recent years, cable-driven robots have begun to attract people's attention. They use cables to replace rigid elements to drive limb movement. They have the characteristics of a large working space, lower motion inertia, strong load-bearing capacity, and good flexibility [13; 14; 15] in multiple scenarios, they can satisfy the rehabilitation needs of different patients. In addition, when the robot is not controlled, the flexible cable can ensure that the patient is not injured. Therefore, cable-driven rehabilitation robots have been widely used in rehabilitation training. [PERSON] et al. [16] developed a new type of cable-driven sports trainingsystem. People need to train on a treadmill, and the traction cable can provide resistance to the legs and effectively improve the movement function of the legs. [PERSON] et al. [17] designed the rehabilitation system that introduces a rigid chain, and experimental research is conducted on the training trajectory of the lower limb traction point in accordance with the planning strategy of rigid body movement. [PERSON] et al. [18] designed a three-degree-of-freedom planar cable-driven robot, which selects single objective optimization to help patients better complete the specified actions of upper limbs. [PERSON] et al. [19] designed a rehabilitation robot combining a cable-driven mobile platform and an adjustable lower extremity exoskeleton device, which can perform rehabilitation training on the waist and lower limbs. [PERSON] et al. [20] developed rigid-flexible hybrid lower limb rehabilitation robot comprehensively considers the cable tension, position of the traction points and system stiffness to study its dynamic stability evaluation method, which provides a consultation for rehabilitation training task planning and control strategies. [PERSON] et al. [21] developed a cable-driven parallel rehabilitation robot for basic movements of the lower limbs. The system consists of a fixed base and a mobile platform that can connect up to six cables. [PERSON] et al. [22] designed a rehabilitation robot that can realize adduction and abduction of lower limbs, and the relationship of human-machine coordinated motion is considered. [PERSON] et al. [23] developed a four-cable traction lower-limb rehabilitation robot for auxiliary training of gait, and the kinematics of the robot was optimized. To improve the adaptability of cable-driven robots, the reconfigurable robots are proposed. [PERSON] et al. [24] designed an adaptive cable-drive system that modifies the pulley arrangement based on the pose of the end-effector to maintain optimal performance. [PERSON] et al.