Direct geometrico-static problem of under-constrained cable-driven parallel robots with three cables

This paper studies under-constrained cable-driven parallel robots with three cables. A major challenge in the study of these manipulators is the intrinsic coupling between kinematics and statics, which must be tackled simultaneously. In this contribution, a general elimination procedure is provided that solves the direct geometrico-static problem, which consists in determining the platform posture and the cable tensions when the cable lengths are assigned. The problem is proven to have up to 156 complex solutions.