This article presents a new topological characterization of the free workspace of manip-ulators moving among obstacles. The free workspace is the set of positions and orienta-tions that the end-effector of the manipulator can reach, according to the joint limits of each of its links, and taking into account the obstacles of the environment. A classification of new connectivity properties of the free workspace is proposed, corresponding to different types of motions (point-to-point motions, following of continuous trajectories) that the manipulator can perform in the Cartesian space. For each property, a necessary and sufficient condition is given, which permits verification of the connectivity of the whole free workspace and leads to all the connected subspaces in it. These properties have been implemented in a Robotics C.A.D. system using octree representation of spaces. Some applications are presented, which show that this work is of primary interest for preparing off-line tasks, and is a new contribution to the problem of robotic cell layout design.