Real-Time Cable Force Calculation beyond the Wrench-Feasible Workspace

Abstract

Under special circumstances, a cable-driven parallel robot (CDPR) may leave its wrench-feasible-workspace. Standard approaches for the computation of set-point cable forces are likely to fail in this case. The novel nearest corner method for calculating appropriate cable forces when the CDPR is outside of its wrench-feasible-workspace was introduced in former work of the authors. The obtained cable force distributions aim at continuity and generate wrenches close to the desired values. The method employs geometrical operations in the cable force space and promises real-time usability because of its non-iterative structure. In a simplified simulation, a cable break scenario was used to carry out more detailed testing of the method regarding different parameters, a higher number of cables, and the numerical efficiency. A brief discussion about the continuity of the method when entering the wrench-feasible-workspace is presented.

Static Workspace Computation for Underactuated Cable-Driven Parallel Robots

“…If the polygon does not exist, 𝝀 is the vertex resulting in a tension distribution closest to wrench feasibility in the Euclidean sense, as in [46]. Analytically speaking, 𝝀 is still described by Eq.…”

An Overview of Cable-Driven Parallel Robots: Workspace, Tension Distribution, and Cable Sagging

“…e paper also proposes a method to evaluate the safety of cable tension distribution results. Boumann and Bruckmann [66] develop a method to find solutions to tension distribution when CDPR operates outside the WFW. Based on geometric analysis, the Nearest Corner Method is used to find the closest solutions that satisfy the equilibrium equation based on detecting the corners of the hypercube composed from the limit of cable tensions.…”

Workspace and Stiffness Analysis of 3D Printing Cable-Driven Parallel Robot with a Retractable Beam-Type End-Effector

“…Thus, the cable length vectors corresponding to the position of the end-effector can be calculated by using the vector loop Equation (1). The use of the proposed end-effector should be investigated by conducting the workspace analysis and stiffness analysis for CDPRs as the workspace analysis of CDPRs has been conducted considering feasible tension distributions for various CDPRs [11][12][13][14]. In addition, the stiffness analysis of CDPRs has been researched for several CDPRs [15][16][17][18].…”

“…Based on the volume change along a specific range of the z-axis, the retracted length can be continuously varied to maximize the overall workspace as the position of the end-effector changes along the z-axis. Thus, the end-effector's retracted length linear function was derived by utilizing an objective function to maximize the volume of the wrench-feasible workspace (Equations (13) and (14)). Figure 10 represents the change of the volume V (z, l e ) according to the changes in the z-axis and the retracted length.…”