Computing Cross-Sections of the Workspace of Cable-Driven Parallel Robots with 6 Sagging Cables

Abstract

To cite this version:Jean-Pierre Merlet. Computing cross-sections of the workspace of cable-driven parallel robots with 6 sagging cables. CK 2017 -Computational Kinematics, May 2017 Computing cross-sections of the workspace of cable-driven parallel robots with 6 sagging cables Abstract. Finding the workspace of cable driven parallel robots (CDPR) with sagging cables (i.e. elastic and deformable cables) is a problem that has never been fully addressed in the literature as this is a complex issue: the inverse kinematics may have multiple solutions and the equations that describe the problem are non-linear and non algebraic. We address here the problem of determining an approximation of the border of horizontal cross-sections of the workspace for CDPR with 6 cables. We present an algorithm that give an outline of this border but also rises several theoretical issues. We then propose another algorithm that allow to determine a polygonal approximation of the workspace border induced by a specific constraint. All these algorithms are illustrated on a very large CDPR.

A Panorama of Methods for Dealing with Sagging Cables in Cable-Driven Parallel Robots

“…Being given the non-algebraic nature of the Irvine equations it seems to be difficult to find an analytic description of the border curve so that we have to rely on a numerical method. For that purpose an efficient approach [13] is to start from a pose X a , that may be arbitrarily chosen as soon as it lies in the workspace, and from one of its IK solutions S ik a . We then moves incrementally the platform along an arbitrary unit vector N by setting the pose X as X] = X a + λ N and solving its IK for a given λ by using the previous IK solution as guess for the Newton method, until we obtain a pose X s such that its current IK solution S ik s has a L j 0 very close to L M 0 so that X s is close to the border.…”

Computing Cross-Sections of the Workspace of Suspended Cable-Driven Parallel Robot with Sagging Cables Having Tension Limitations

“…But the discretisation approach used in this paper is not efficient, especially for large robot, and several theoretical issues have not been addressed. We have proposed a preliminary analysis of this problem for 6 d.o.f robot [18] with the purpose of showing that calculating workspace slices may lead to complex workspace with a large number of disconnected components but the proposed algorithm was computer intensive and was also relying on discretisation.…”