# Kinematic Analysis and Motion Planning of Cable-Driven Rehabilitation Robots
## 1 Introduction
[25] designed a reconfigurable suspended cable-driven robot for aircraft maintenance and obtained the optimal configuration of the robot by solving a multi-objective optimization problem. [PERSON] et al. [26] designed a discrete reconfigurable planning method for an 8-6 cable-driven robot that uses [PERSON]'s algorithm to select the best reconfiguration strategy. There is also some research on the configurable aspects of cable-driven rehabilitation robots. MariBot is a 5-degree-of-freedom serial-parallel robot, two rotational joints of serial structure provide a wide horizontal range of upper limb movement [27]. [PERSON] et al. [28] designed the cable-driven exoskeleton robot; they optimized the positions of the cable connection points by using the deviation area between the actual and desired trajectory of the robot arm as the optimization objective. Sophia-3 is an adaptive cable-driven device with a tilting working plane, which can achieve excellent force capabilities with fewer cables by moving the pulley lock [29]. Through the comprehensive analysis of the above research, it is found that the proposed cable-driven rehabilitation robots do not consider the compliance of rehabilitation trajectory from the perspective of human joints, and the designed cable exit points only move in a single direction. For these reasons, according to the tasks and characteristics of rehabilitation, this study comprehensively considers the angle flexibility of human joints and the configurability of cable exit points. A new trajectory planning method is proposed, which is used to improve joint flexibility. The cable exit points can move in two directions, and the cable exit points can rotate according to the direction of the cable, which effectively improves the workspace. Compliant action can improve the patient's comfort and promote early recovery; therefore, it is very important to plan the rehabilitation trajectory reasonably during the rehabilitation training process. In the early stage of rehabilitation, robots need to provide auxiliary motion suitable for human rehabilitation on the basis of the characteristics the of human body structure. Therefore, kinematic analysis and trajectory planning simulation of the robot need to be carried out in advance [30]. The model of a cable-traction lower limb is similar to a multilink cable-driven manipulator. [PERSON] et al. [31] proposed a systematic method for determining the tensionable workspace of a multibody cable-drive mechanism, the method is applied to several single-degree-of-freedom and two-degree-of-freedom mechanisms with different cable distributions. [PERSON] et al. [32] proposed a generalized model of a multilink cable-driven serial manipulator and derived the kinematics and dynamics of the generalized model based on the cable-routing matrix. Inthis study, a new type of cable-driven rehabilitation robot is conceived. Its cable exit point can move on the rail brackets in two directions and can provide rehabilitation training of various postures. To achieve a better rehabilitation effect, the relationship between the change in the human joint angle and the change in cable length is analyzed, and a new trajectory planning method is presented. Simulation and experiments verify the effectiveness and feasibility of this method.