The base of free-floating manipulators is not inertially fixed. For these manipulators, the linear and angular momentum are conserved. The linear momentum equations are holonomic while the angular momentum equations are nonholonomic. The presence of nonholonomic constraints makes the path-planning schemes, commonly used for fixed-base manipulators, unsuitable for free-floating manipulators. In this paper, we first apply inverse position and inverse rate kinematics path-planning schemes to a free-floating closed-chain planar manipulator and show that these schemes have shortcomings. Then, a working path-planning scheme is described which is based on careful study of the rate kinematics of the free-floating closed-chain manipulator. This algorithm is implemented and the graphical simulations are presented.