## 2 Magnetic Mechanism and Control System for a Wireless Operation
### Analysis of the Electromagnetic Control System  
For wireless assistive finger movement, we developed an electromagnetic control system. The proposed driving system consists of a driving coil and permanent magnet array (M3) to generate the driving magnetic force. M3 was positioned in the inner space of the driving coil. Figure 3a shows the results of a COMSOL magnetic simulation of the combined magnetic field distribution from the magnets with the coil at the driving current of \(\pm\) 25 A. When a 25 A current is applied, the coil becomes an electromagnet with the top and bottom as the N and S poles, respectively. Thus, the electromagnet polarity is opposite to that of M3, and there is a very low-strength magnetic field in the M3 region. However, the overall magnetic field distribution is directed upward of the coil, causing the finger flexion. When a \(-\)25 A current is applied, the polarity direction is the same for both the electromagnet and the magnet array.  
Figure 3: Control–system analysis using a magnetic simulation and magnetic field measurement: (**a**) simulation results including M3 at 25 and \(-\)25 A; (**b**) developed 3-axis measurement system and LabView-based instrumentation software; (**c**) measured magnetic field distributions with \(-\)25 and 25 A driving currents at 66 mm high initial hand position (the \(-\)25 A case produced a stronger field distribution because of the M3 direction); (**d**) field distributions for \(-\)25 and 25 A at 96 mm height (the height indicates the finger position at 90\({}^{\circ}\)).  
In this case, the flux is directed from the coil top to the bottom and the field direction causes finger extension. Through the magnetic simulation performed in this study, we could predict the field distributions generated in the working space by the coil and magnet array. In conjunction with the simulation, we measured the actual magnetic field distributions using a gauss meter (F.W. Bell 5180 Milwaukie, OR, USA). Note that we developed a tailored measurement system involving both hardware and software, as shown in Figure 3b. The employed hardware was a 3-axis auto-scanning machine, in which the measuring probe could be moved with a minimum measurement distance of 1 mm. In this measurement, the XY plane was measured at 5 mm intervals, and the height (Z-axis) was measured at 10 mm intervals from the surface to a maximum of 100 mm. The measured data were transformed into a three-dimensional magnetic field distribution in the measurement program. In this system, the hand is positioned at a 66 mm height from the coil because this corresponds to the hand rest height. Therefore, the highest possible point of the finger trajectory was 100 mm. Figure 3c shows magnetic field distributions obtained for \(-25\) A and 25 A applied currents at a height of 66 mm from the driving coil. It is apparent that the \(-25\) A and 25 A currents generate average field strengths of 31.877 and 19.635 kA/m, respectively, in the working space.  
As designed, the negative current in the driving coil generates a magnetic field in the same direction as that from the magnet array, whereas the positive current generates a magnetic field in the opposite direction to that of the magnet array. Therefore, the field distribution of 25 A is lower than that of \(-25\) A. The applied \(-25\) and 25 A currents induce maximum extension and flexion, respectively. Figure 3d shows magnetic field distributions at 96 mm height when the applied currents were \(-25\) and 25 A, respectively, yielding average field strengths of 17.367 and 14.769 kA/m, respectively. The 66 and 96 mm heights correspond to maximum finger extension and flexion, respectively. Thus, the magnetic field strength due to the two maximum currents (\(\pm 25\) A) correspond to the maximum system driving range.