The exploration and inspection of narrow spaces in nuclear facilities require the use of long-reach manipulators. Coupled tendon-driven manipulators can realize lightweight and slender arms by positioning actuators, such as motors, at the base. Currently, we are developing a coupled tendon-driven super long-reach articulated arm, which we name “Super Dragon.” Super Dragon is a robot arm with a total length of 10 m, a maximum arm diameter of 0.2 m, and 10 joints. In this paper, we focused on the elasticity and elongation of ropes. The joint actuation of Super Dragon utilizes synthetic fiber ropes characterized by their high strength and flexible bending. However, when these ropes are used over long lengths, wire elongation occurs, thus causing the joint angles to exhibit unintended and unstable behavior. Therefore, we focused on a specific posture and employ a double pulley as a mechanical solution to suppress unstable behavior. We introduced stability criteria and performed parametric searches to obtain the appropriate double pulley radii. Subsequently, we identified the position and radius of the introduced double pulley that can be analytically stabilized. By installing a double pulley in the actual machine and conducting experiments, we successfully suppressed the unstable behavior.