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This paper investigates the kinematics of free-floating space robots during motion planning for target capture. First, generalized kinematic mapping of free-floating space robots with open-chain multibody structures is established. To predict the reaction movement of spacecraft caused by the motions of its manipulators, a dynamic coupling matrix concept, the main contribution of this paper, is proposed to explicitly express position kinematics. The feasibility and effectiveness of the presented numerical implementation algorithms are then verified by solving forward and inverse kinematics problems. Then, applications in workspace analysis and motion planning are described. Finally, a discussion of the framework is presented.