On the trilaterable six-degreeof-freedom parallel and serial manipulators

Abstract — The inverse/direct kinematics of trilaterable se-rial/parallel manipulators can be stated as a system of distance constraints whose set of solutions can be determined using a sequence of trilaterations, possibly involving points at infinity. It is possible to decide whether a mechanism is trilaterable by relying only on its topology. Based on this fact, we here enumerate all trilaterable serial and in-parallel robots with six degrees of freedom. The relevance of the obtained family of manipulators is established when it is shown to contain the best-known commercial serial robots. As a result of this analysis, we come up with a general method to solve the inverse/direct kinematics of a wide family of manipulators. Index Terms — Trilateration, Cayley-Menger determinants, position analysis of robots. I