This article presents a new geometric analysis of the free work space of a robot among obstacles. The free work space (FW) is defined as the set of positions and orientations that the robot's end effector can reach, according to the joint limits and the various obstacles lying in the environment. The aim is to give global descriptions of the robot's ability to move in the operational space (which coincides with Carte-sian space when only position coordinates are specified). The main contribution of this work is the characterization of the effects of obstacles on the work space geometry, as well as on its topology. The ability of a robot to move freely in its work space (called the "moveability") is difficult to describe and needs stringent formalizations. The concept of move-ability is introduced through various properties and their corresponding necessary and sufficient conditions. Using a Constructive Solid Geometry (CSG) Computer-Aided Design (CAD) description of robots and obstacles and an octree model of the FW, these properties permit characterization of selected moveability areas in the FW, where, for instance, any n points can be linked together or where any continuous trajectory can be achieved without changing configuration. This new global description is of great interest for the user of CAD systems when designing robotic cells.