Dynamic and Wrench-Feasible Workspace Analysis of a Cable-Driven Parallel Robot Considering a Nonlinear Cable Tension Model

Cable-driven parallel robots (CDPRs) have several advantages and have been widely used in many industrial fields, especially industrial applications that require high dynamics, high payload capacity, and a large workspace. In this study, a design model for a CDPR system was proposed, and kinematic and dynamic modeling of the system was performed. Experiments were carried out to identify the dynamic modulus of elastic cables based on the dynamic mechanical analysis (DMA) method. A modified kinematic equation considering cable nonlinear tension was developed to determine the optimal cable tension at each position of the end-effector, and the wrench-feasible workspace was analyzed at various motion accelerations. The simulation results show that the proposed CDPR system obtains a large workspace, and the overall workspace is satisfactory and unrestricted for moving ranges in directions limited by the X-axis and the Y-axis from −0.3 to 0.3 m and by the Z-axis from 0.1 to 0.7 m. The overall workspace was found to depend on the condition of acceleration as well as the moving ranges limited by the end-effector. With an increase in external acceleration, the cable tension distribution increased and reached a maximum in the case of 100 m/s2.

Kinematic uncertainty analysis of a cable-driven parallel robot based on an error transfer model

Cable-driven parallel robots (CDPRs) are a kind of mechanism with large workspace, fast response, and low inertia. However, due to the existence of fixed pulleys, it is unavoidable to bring uncertain cable lengths and lead to pose errors of the end-effector (EE). The inverse kinematic model of a CDPR for picking up medicines is established by considering radii of fixed pulleys. The influence of radii of fixed pulleys on errors of cable lengths is explored. Error transfer model of the CPDR is constructed, and uncertain sources of cable lengths are analyzed. Based on evidence theory and error transfer model, an evidence theory-based uncertainty analysis method (ETUAM) is presented. The structural performance function for kinematic response is derived based on error transfer model. Belief and plausibility measures of joint focal elements under the given threshold are obtained. Kinematic error simulations show that errors of cable lengths become larger with the increase of radii of fixed pulleys. Compared with the vertex method and Monte Carlo method, numerical examples demonstrate the accuracy and efficiency of the ETUAM when it comes to the kinematic uncertainty analysis of the CDPR.

Modal Kinematic Analysis of a Parallel Kinematic Robot with Low-Stiffness Transmissions

Several industrial robotic applications that require high speed or high stiffness-to-inertia ratios use parallel kinematic robots. In the cases where the critical point of the application is the speed, the compliance of the main mechanical transmissions placed between the actuators and the parallel kinematic structure can be significantly higher than that of the parallel kinematic structure itself. This paper deals with this kind of system, where the overall performance depends on the maximum speed and on the dynamic behavior. Our research proposes a new approach for the investigation of the modes of vibration of the end-effector placed on the robot structure for a system where the transmission’s compliance is not negligible in relation to the flexibility of the parallel kinematic structure. The approach considers the kinematic and dynamic coupling due to the parallel kinematic structure, the system’s mass distribution and the transmission’s stiffness. In the literature, several papers deal with the dynamic vibration analysis of parallel robots. Some of these also consider the transmissions between the motors and the actuated joints. However, these works mainly deal with the modal analysis of the robot’s mechanical structure or the displacement analysis of the transmission’s effects on the positioning error of the end-effector. The discussion of the proposed approach takes into consideration a linear delta robot. The results show that the system’s natural frequencies and the directions of the end-effector’s modal displacements strongly depend on its position in the working space.

Rapid and safe wire tension distribution scheme for redundant cable-driven parallel manipulators

A non-iterative analytical approach is investigated to plan the safe wire tension distribution along with the cables in the redundant cable-driven parallel robots. The proposed algorithm considers not only tracking the desired trajectory but also protecting the system against possible failures. This method is used to optimize the non-negative wire tensions through the cables which are constrained based on the workspace conditions. It also maintains both actuators’ torque and cables’ tensile strength boundary limits. The pseudo-inverse problem solution leads to an n-dimensional convex problem, which is related to the robot degrees of redundancy. In this paper, a comprehensive solution is presented for a 1–3 degree(s) of redundancy in wire-actuated robots. To evaluate the effectiveness of this method, it is verified through an experimental study on the RoboCab cable robot in the infinity trajectory tracking task. As a matter of comparison, some standard methods like Active-set and sequential quadratic programming are also presented and the average elapsed time for each method is compared to the proposed algorithm.