Inverse Geometrico-Static Analysis of Under-Constrained Cable-Driven Parallel Robots with Four Cables

This paper presents the inverse geometrico-static analysis of under-constrained cable-driven parallel robots with 4 cables. The problem consists in finding all equilibrium configurations of the end-effector when either its orientation or the center-of-mass’s position is assigned. In both cases, a further point of the end-effector is constrained to lie on a given plane. A major challenge is posed by the intrinsic coupling between kinematics and statics, which must be tackled simultaneously. The problems at hand are solved by analytical elimination procedures, thus leading to univariate polynomials free of spurious factors. All potential solutions may be real.