The Dimensional Synthesis of Spatial Cable Driven Parallel Mechanisms

Abstract

This paper presents a method for the dimensional synthesis of fully constrained spatial cabledriven parallel mechanisms (CDPMs), namely, the problem of finding a geometry whose wrenchclosure workspace (WCW) contains a prescribed workspace. The proposed method is an extension to spatial CDPMs of a synthesis method previously published by the authors for planar CDPMs. The WCW of CDPMs is the set of poses for which any wrench can be produced at the endeffector by nonnegative cable tensions. A sufficient condition is introduced in order to verify whether a given sixdimensional box, i.e., a box covering pointpositions and orientations, is fully inside the WCW of a given spatial CDPM. Then, a nonlinear program is formulated, whose optima represent CDPMs that can reach any point in a set of boxes prescribed by the designer. The objective value of this nonlinear program indicates how well the WCW of the resulting CDPM covers the prescribed box, a null value indicating that none of the WCW is covered and a value greater or equal to one indicating that the full prescribed workspace is covered.