Direct Geometrico-static Problem of Underconstrained Cable-Driven Parallel Robots With $n$ Cables

The direct geometrico-static problem of cable-driven parallel robots with 5 cables is presented. The study provides procedures for the identification of all equilibrium poses of the end-effector when cable lengths are assigned. A leastdegree univariate polynomial in the ideal governing the problem is obtained, thus showing that the latter has 140 solutions in the complex field. By a continuation technique, an upper bound on the number of real solutions is estimated. An algorithm based on parameter homotopy continuation is developed for the efficient computation of the whole solution set, including equilibrium poses with slack cables.