# Dynamic Modeling and Optimization of Tension Distribution for a Cable-Driven Parallel Robot
## 1 Introduction  
Cable-driven parallel robots have many advantages over other robots driven by traditional styles such as mechanical, hydraulic, or pneumatic modes. This is because traditional-driven styles have the same defect, which is that the motion range of the end-effector is significantly limited [1]. In contrast, the CDPR allows the end-effector to move rapidly in a large space due to its drive characteristics [2; 3; 4]. By adjusting the cable tension, the cable-driven parallel robot has the advantages of high load capacity, broad working space, and low motion inertia [5; 6]. Therefore, it is widely used in many fields, such as industrial lifting [7], medical rehabilitation [8; 9], tactile interaction [10], and 3D printing [11; 12]. Scholars were committed to studying the related issues of the cable tension distribution algorithm for cable-driven parallel robots. [PERSON] proposed a new two-loop dynamic control scheme, which introduced the parallel two-loop tracking strategy and provided a more compatible scheme but did not take into account the real-time performance of the cable tension method [13]. [PERSON] studied the mechanical characteristics of a cable-driven lower limb rehabilitation robot (CDLR). The mechanical properties of cable-driven lower limb rehabilitation robot (CDLR) were designed and studied. [14]. [PERSON] used a non-iterative, two-degree-of-freedom-driven redundant CDPR real-time cable tension distribution algorithm to solve the cable tension [15]. Based on the feasible polygon of CDPR and its stiffness matrix, [PERSON] selected a set of allowable cable tensions to minimize the movement of the platform displacement [16]. [PERSON] employed a new methodfor the distribution of positive tension in cable-driven parallel robots. In the method, a nonlinear disturbance observer was introduced to eliminate kinematic uncertainties caused by redundant resolution [17]. However, the above studies only focused on analyzing the tension calculation, and there is little research on tension distribution optimization. Additionally, some tension calculation methods had certain defects, such as discontinuity. In order to optimize the tension distribution of a planar parallel robot driven by four cables, [PERSON] took advantage of the quadratic programming algorithm and the dynamic model to deal with the optimization problem [18]. [PERSON] established a system dynamics model considering wave excitation to improve the positioning accuracy and anti-interference ability of the moving platform with the end-effector installed. Further, he studied the controllable workspace and cable tension optimization algorithms [19]. [PERSON] has developed an improved kinematic equation that takes into account the nonlinear tension of the cable based on a dynamic mechanical analysis (DMA) method to determine the optimal cable tension at each position of the end actuator [20]. CaoSheng provides a tension function containing a hyperbolic tangent function, which can simultaneously implement the necessary wrench and the appropriate tension distribution and manage the tension distribution optimization [21]. These four studies only analyzed the tension optimization of the cable-driven parallel structure with four cables and three degrees of freedom but did not optimize the tension of the cable-driven parallel mechanism with more than four degrees of freedom and did not consider the influence of system stiffness on cable tension optimization. [PERSON] presents an algorithm that can be used to calculate the cable tension distribution of a cable-driven parallel robot with arbitrary redundancy and gives the formula for the cable tension distribution in the form of an analytic solution. However, the algorithm may not be solved in some cases [22; 23]. [PERSON] et al. proposed a cable force distribution of an n-DOF parallel robot driven by n + 2 cables. Taking a 6-DOF 8-cable-driven parallel robot system as an example, by introducing two random variables, the cable tension was expressed as the equation of these two random variables.