Geometrically exact three-dimensional modeling of cable-driven parallel manipulators for end-effector positioning

A geometrically exact analytical model of cable-driven parallel manipulators operating in a three-dimensional space is formulated and discussed this work. The aims at investigating the positioning rigid body Cartesian by m-cables-driven manipulator taking into account cables mass, their elasticity and, consequently, sag effect. direct kinematic problem means 3(m+1) nonlinear equations expressing compatibility equilibrium same number unknowns, namely, 3m components constraint reactions 3 finite rotations. novel approach to solution inverse adding set m target obtain 4m+3 algebraic solved terms an equal unknowns. latter are defined increments variables additional i.e., cable unstretched lengths. elastostatic point mass end-effector then derived. Consequently, problems 4m equations, respectively, Examples with increasing considered, showing that, although solving may imply very slack configurations, proposed allows find solution.