Spatial transformation-based method for solving wrench-feasible workspace of cable-driven parallel robots

FENG Yongli; HE Mingyuan; YU Jiangtao; LI Desheng; HUANG Baowang; WANG Hongkai

doi:10.16578/j.issn.1004.2539.2026.07.007

Abstract：[Objective]Aiming at the problem of identifying the implicit boundaries of workspace for cable-driven parallel robots(CDPRs),a novel method based on spatial transformation was proposed to solve the available wrench set(AWS)and wrench-feasible workspace(WFW).[Methods]Firstly,kinematic and static models of the CDPR were established by neglecting cable mass and sag.Based on the structure matrix,a spatial transformation matrix mapping the wrench space to the cable force space was derived,which transformed the non-orthogonal bases into a set of unit orthogonal bases.Secondly,by applying the inverse mapping of a hyper-rectangular polyhedron from the cable force space back into the wrench space,the pose-dependent actual AWS of the robot was determined.Furthermore,the required wrench set(RWS),represented as a hyper-rectangular polyhedron in the wrench space,was transformed into the cable force space.Based on the concept of polyhedral containment within the orthogonal cable force space,the complex non-linear workspace boundaries were converted into explicit linear inequality constraints,thereby identifying the WFW of the robot.Finally,numerical simulations on an 8-cable-driven 6-degree-of-freedom redundant parallel robot were conducted to verify the mathematical accuracy of the proposed scheme.[Results]Simulation results demonstrate that the proposed spatial transformation scheme effectively constructs the multi-dimensional convex hull mesh and accurately identifies the six-dimensional WFW under various Euler angle orientations.The topologically simulated trajectories show that the volume and geometry of the WFW are highly coupled with the mechanical architecture,symmetric layout angles of the cables,and the allowable cable tension limits.The research findings provide a basis for configuration optimization and precise trajectory planning of flexible parallel robots.