arXiv:2610.22558v1 Announce Type: new Abstract: Motion of a robotic manipulator mounted on a free-floating spacecraft induces base translation and rotation, creating a dynamic coupling that affects end-effector motion. This paper characterizes that coupling in a planar three-link space manipulator. Using momentum conservation, velocity mappings are developed between manipulator joints, the end effector, and the spacecraft base. Singular value decomposition is then used to examine coupling strength, directional anisotropy, and the orientation of the coupled motions. Numerical maps show that coupling strength is invariant to the first joint angle but depends strongly on the relative configuration of the remaining joints. Increasing the spacecraft base mass reduces joint-to-base and end-effector-to-base coupling, while its effect on the joint-to-end-effector mapping is smaller and more dependent on configuration. The translational end-effector-to-base mapping is highly anisotropic in some configurations: its base-velocity ellipse becomes increasingly flattened as the weak coupling mode approaches zero. The principal end-effector and base velocity directions also change their relative alignment across the configuration space, producing predominantly opposing responses in some regions and transverse or approximately codirectional responses in others. Together, these results provide a geometric description of how coupling magnitude and direction vary with manipulator configuration and spacecraft mass.