— Humans have at some point learned an abstraction of the capabilities of their arms. By just looking at the scene they can decide which places or objects they can easily reach and which are difficult to approach. Possessing a similar ion of a robot arm’s capabilities in its workspace is important for grasp planners, path planners and task planners. In this paper, we show that robot arm capabilities manifest themselves as directional structures specific to workspace regions. We introduce a representation scheme that enables to visualize and inspect the directional structures. The directional structures are then captured in the form of a map, which we name the capability map. Using this capability map, a manipulator is able to deduce places that are easy to reach. Furthermore, a manipulator can either transport an object to a place where versatile manipulation is possible or a mobile manipulator or humanoid torso can position itself to enable optimal manipulation of an object.