The motion of a free-floating space robot is characterized by the principle of conservation of angular momentum. It is well known that these angular momentum equations are nonholonomic, i.e., are nonintegrable rate equations. If the base of the free-floating robot is partially actuated, it is difficult to attain trajectories of the joints that result in point-to-point motion of the entire robot system in its configuration space. However, if the drift-less system associated with the angular momentum conservation equations is shown to be differentially flat, point-to-point maneuvers of the free-floating robot in its configuration space can be constructed. However, an open research problem in the current literature is to show the property of differential flatness for a general space robot. The primary contributions of this paper are as follows: (i) study systematically the structure of the nonholonomic rate constraint equations of a free-floating open-chain space robot with arbitrarily oriented joints and two momentum wheels; (ii) establish the design conditions under which the system exhibits differential flatness; (iii) exploit these design conditions for point-to-point trajectory planning and control of the space robot