CHARACTERIZATIONS OF FULLY CONSTRAINED POSES OF PARALLEL CABLE-DRIVEN ROBOTS: A REVIEW

The pose of the mobile platform of a parallel cable-driven robot is said to be fully constrained if any wrench can be created at the platform by pulling on it with the cables. A fully constrained pose is also known as a force-closure pose. In this paper, a review of three useful characterizations of a force-closure pose is proposed. These characterizations are stated in the form of theorems for which proofs are presented. Tools from linear algebra allow to derive some of these proofs while the others are more difficult and can hardly be obtained in this manner. Therefore, polyhedral cones, which are special cases of convex cones, are introduced along with some of their well-known fundamental properties. Then, it is shown how the aforementioned difficult proofs can be obtained as direct consequences of these properties.