For a robotic arm consisting of numerous rigid linkages, the configuration space consists of the location of each linkage (taken to be a rigid body, as in the section above), subject to the constraints of how the linkages are attached to each other, and their allowed range of motion. Thus, for n linkages, one might consider the total space [ R 3 × × S O ( 3 ) ] n except that all of the various attachments and constraints mean that not every point in this space is reachable. Thus, the configuration space Q is necessarily a subspace of the n -rigid-body configuration space.