In this paper, we propose an efficient motion planning method for fast motion of path tracking task with constant hand speed using redundant manipulator. The proposal method performs path finding on a state space of the manipulator instead of a motion planning. We previously proposed a motion planning method for fast motion of path tracking task with constant hand speed. However, this motion planning method had required long calculation time. Therefore, we propose an efficient motion planning method that based on partitioning the hand path into difficult sections and easy sections to do different path finding method on each sections. The difficult sections are the sections that difficult to operate fast motion within joint torque limits and joint velocity limits. The easy sections are the sections that easy to operate fast motion within the limits. In difficult sections, we look for paths to avoid limits on the state space using the previous method. In easy sections, we derive the connective paths between planned paths on the difficult sections. The 3-link planar manipulator has been used to show the efficacy of proposed method.