Inverse 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, general elimination procedures are provided that solve the inverse geometrico-static problem with assigned orientation or position. In the former case, the platform orientation is given, whereas the platform position and the cable lengths and tensions must be computed. In the latter case, the platform position is known, whereas the platform orientation and the cable lengths and tensions must be calculated. These problems are proven to admit up to 1 and 24 real solutions, respectively.