Path planning is necessary for free-floating space manipulators to perform space tasks. However, the coupled motion between manipulator and base directly acts on path planning procedure, which results in current manipulator motion state is dependent on previous motion state, so we must consider the control of base-coupled motion in path planning. In this paper, we propose a general path planning strategy for free-floating space manipulators based on the representation space (RS) analytical method. RS consists of the representation variables which are connected to task attributes and base-coupled motion simultaneously, and it can be utilized to check task realizability and construct a path planning domain for free-floating space manipulators. To analyze the effects of base-coupled motion on path planning, we classify RS into five types according to different base control modes: fixed vehicle RS (FRS), attitude constrained RS (CRS), maximum reachable RS (MRS), guaranteed RS (GRS), and partly guaranteed RS (PGRS). CRS tells us the variation of base attitude (instead of base centroid position) directly influences task realizability and path planning, so we should particularly consider the control of motion of base attitude in path planning. With appropriately considering the control of base attitude and satisfying the base attitude deflection limitation, only PGRS can be utilized to check task realizability and construct a path planning domain for free-floating space manipulators. Then, we design a path planning strategy in PGRS based on A * algorithm. Finally, we apply the RS analytical method to the 3-DOF free-floating space manipulator to visually show RS, and the effectiveness of the method is verified by a simulation experiment. The RS analytical method is appropriate to path planning for any kinds of manipulators and various tasks. We only need to select the suitable representation variables, which can faithfully reflect task and manipulator attributes.