In previous research, we designed a grasp-Training robot for the post-stroke patient in relation to its usability and wearability for ease of use in clinical practice. Experimental results obtained from a post-stroke patient showed that by combining a grasping support of the robot and the mechanism for pushing an elastic bar on the palm, the grasping reflex was induced in paralyzed patient in a clinical test that involves measuring EMG signals. However, the robot has one structural issue that subjects could not use the robot without fixing subjects' wrist joint, then the robot could not realize synergistic movement of the wrist and the fingers. In this paper, we introduced the new mechanism that can extend the wrist joint into the previous robot having the glove type device. New mechanism is designed by imitating a mechanism of the bascule bridge. We introduced the wire drive system having one motor and the stepped shaft for pulling wires. As the shaft has steps, the shaft can pull different amount of wires for the glove type device and the wrist movement mechanism, then the robot can realize the extension of the wrist and the flexion of the fingers as a cooperative motion.