## 1 Introduction  
Cable-driven parallel robots (CDPRs) use flexible cables to control an end effector by winding and unwinding cables instead of using the rigid links of common parallel robots. The use of light cables with high load-withstanding ability as actuators can reduce the actuator weight as well as the inertia; thus, CDPRs have many typical advantages, such as high dynamics, low inertia, and large workspaces. Due to these advantages, CDPRs have been widely used in various fields, such as in radio telescopes [1], multiple mobile crimes [2], waist rehabilitation [3], and construction cable robots [4]. The CDPR system has also been studied by researchers from different perspectives. The control algorithm is an important factor affecting the accuracy and stability of the robot system. To ensure the stability of the end-effector during movement, the use of a hybrid position-force control algorithm as an asynchronous control of the cable force was proposed [5]. A passivity-based control for a planar cable-driven manipulator system was also investigated. In this work, to simplify the modeling process of the system, a lumped-mass model is used, and each cable is modeled individually. Then, the derivation of [PERSON]'s equation and the null-space method is used to derive the dynamics of the system [6]. To dynamically control CDPRs in [7], visual feedback with linearizing inner loop control was proposed, and this new approach allows for the control of CDPRs when using long cables or polymer cables. In addition, the stability of the dynamic control scheme was demonstrated usingTikhonov's theorem. Characteristics of the cable used for CDPR that are related to the accuracy of the end-effector were also considered based on nonlinear viscoelastic properties, such as structural elongation and hysteresis. Therefore, to improve the accuracy, many studies have considered these attributes. Rather than the commonly used elastic cable approach, an approach based on the numerical analysis of cable elements was proposed in [8], where a novel formulation for three-dimensional cables was developed. Besides that, the thermal-elastic of the proposed element was also analyzed. The proposed formulation leads to an explicit stiffness matrix this makes the new element more efficient in terms of the analysis time, and the research results in the literature indicate the advantages of the proposed scheme. Moreover, a simple model for cable elongation was incorporated to increase position accuracy for CDPR [9]. A hysteresis model was developed based on the Bouc-Wen model, and dynamic behavior, such as static creep, hardening effects, long-term recovery, and hysteresis, was described based on a viscoelastic model with only an integrated dynamic model [10; 11; 12]. However, to evaluate its performance, the workspace analysis of a CDPR, considering the condition of various accelerations, is an important issue. The workspace of CDPR can be divided into two categories: dynamic and static [13]. The static workspace can be further divided into a wrench-closure workspace. Most of the research on CDPR has only considered a static condition in the analysis of the workspace. A workspace analysis under equilibrium conditions to evaluate external force was presented in [14]. Besides, a force-closure workspace analysis of CDPR was conducted based on a workspace with fully restrained positioning mechanisms. Because of the maintenance of positive cable tension, the general algorithm to generate a force-closure workspace was studied at various orientations of the end-effector [15]. Moreover, a method that is seen as one of the most efficient interior-point methods was improved in [16] to analyze the wrench-feasible workspace for general CDPR. This method uses the linear matrix inequalities and the projective method to obtain the wrench-feasible workspace. In [17], to analyze the wrench-feasible printing workspace, a methodology that considers the impact of cable mass and end-effector orientation was proposed.