Maximal cable tensions of a N-1 cable-driven parallel robot with elastic or ideal cables

Abstract : Determining what will be the maximal cable tensions of a cabledriven parallel robot (CDPR) when it moves over a given workspace is an important step in the design phase as it will allow to choose the cable diameter and to provide a requested information for tuning the CDPR actuation. In this paper we consider a suspended N-1 CDPR with n cables where all cables are attached at the same point, which leads to a 3-dof robot. We assume a quasi-static behavior of the robot and assume that the cable are either ideal or elastic so that we neglect the sagging effect. Under these assumption we show that the maximum of the cable tensions may be determined in a very fast way by solving a set of secondorder polynomials which will lead to the poses at which the maximum of each cable tension will occur. For example for a four-cables CDPR determining the maximal cable tension requires to solve at most 149 second order polynomials.