## 4 Discussion and Conclusions  
The developed devices and control system generate magnetic force and torque for wireless assistive finger training. In our previous work, we focused on the development of the wireless driving method, but the resultant system could not exercise multiple fingers simultaneously. In this study, we used the wireless driving concept developed in the previous study to verify the proposed device and their performance. Hence, it was confirmed that the device can move four fingers simultaneously for flexion and extension motion. The fabricated device has the advantage of generating natural finger movement. To validate the developed driving system, we developed a device and measurement software that can scan and measure the magnetic field in three dimensions. In addition, by using a video-based real-time observation system, we can observe movement trajectories during hand movements for quantitative motion analysis. The device was designed to prevent interference between the magnets on the fingers and generate natural finger movement. In particular, in the fabricated multi-link magnet device, the magnets are installed inside four containers; therefore, the coupling between these magnets is very important. To determine the appropriate setup, the numbers of magnets installed in the various containers were determined through simulation and experiment. Note that the natural hand motion (flexion) is disturbed if the magnetic force between the containers is large. However, it was confirmed that the proposed structure, mechanical elements, and the balanced magnetic coupling maintain a natural finger posture. Stroke patients have difficulty maintaining natural finger posture. Thus, the proposed device is very important. Furthermore, the device provides natural flexion and extension according to changes in magnetic field strength and direction, allowing wireless operation. In addition, the overall system configuration allows application as a passive training device. That is, if the patient's hand has muscle strength, they can exercise this strength using the magnetic coupling force \(F_{M1,2}\) and \(F_{M1,3}\) without \(F_{M1,E}\), i.e., applying the system as a passive training device. The developed devices are lightweight, have very simple structures and configuration, and have good wearability on the hand as they do not act as a load. In fact, these features are most important for training or rehabilitation devices or systems. In particular, the magnetic force and torque can provide wireless actuation of the two devices because of these features. Finally, because of the height of the hand rest, the magnetic force for the flexion motion was decreased. By reducing the height of the hand rest or increasing the driving current, we can increase the magnetic force for finger flexion (\(F_{M1,E}\)). We have proposed devices and a control system (including a motion tracking system) for wireless finger training. In the proposed control system, the hand position must be fixed for finger training because a single driving coil is used. Therefore, we are developing a three-axis coil-based control system for more convenient assistive finger training. By sensing the hand position, the control system will automatically change the driving coil or the current phase to generate a magnetic field suitable for the flexion and extension of the hand in the given position. [PERSON] designed and conducted experiments and wrote and edited the manuscript. [PERSON]-[PERSON] and [PERSON]-[PERSON] obtained resources, provided the main idea for the control method and system configuration, and verified the implemented system and edited the manuscript. All authors have read and agreed to the published version of the manuscript.