Under-Constrained Cable-Driven Parallel Robots

This paper studies cable-driven parallel robots with less than six cables, in crane configuration. A major challenge in the study of these manipulators is the intrinsic coupling between kinematics and statics, which must be dealt with simultaneously. A geometrico-static model is provided, together with a general procedure aimed at effectively solving the inverse and direct position problems. The stability of equilibrium is assessed within the framework of a constrained optimization problem, for which a purely algebraic formulation is provided. A spatial robot with three cables is studied as an application example.