## 3 Magnetic Device Analysis and Results
### Motion Analysis of Multi-Link Magnet Device
Furthermore, we observed the force generated during hand movement according to changes in the driving current and finger angle, as shown in Figure 8. For the force analysis, we analyzed the results for the maximum bending point by dividing them into sections to match the trajectory of motion. As mentioned above, Figure 8a,b shows the trajectories for the divided sections obtained with and without M2. The results indicate that, when the driving current is changed from 25 to \(-\)16 A in Section A1, the finger angle (finger device) is maintained at approximately 170\({}^{\circ}\) and the generated force changes from 0.651 to 0.034 N, as shown in Figure 8c1. The applied positive current produces two forces that can be summed (\(F_{M1,2}+F_{M1,E}\)) in Section A1, whereas the negative current causes the decreased driving force because of the corresponding force difference (\(F_{M1,2}-F_{M1,E}\)). Note that, because of  
Figure 7: Observation of motion trajectory (the red line is an extension motion trajectory and the black line is a flexion motion trajectory): (**a**) device configuration and total range of movement; (**b**) trajectory of motion from \(-\)25 A to 25 A; (b1–b12) finger positions without M2 on palm; (**c**) device configuration and total range of movement including M2; (**d**) trajectory of motion for overall system, where d1–d3 show the finger positions according to variations in the driving current. the bending-motion holding section according to changes in the driving current, the acting force tends to gradually decrease as the current changes. Section A2 corresponds to the range in which the bending motion changes to a stretching motion, as the driving current moves from \(-16\) to \(-25\) A. In this section, the change in motion (finger angle) is very fast compared to the change in driving current because of the driving force variations, as shown in Figure 8c2. When the finger angle is \(170^{\circ}\) to \(50^{\circ}\), the rate of change of \(F_{M1,E}\) is low and the average force is approximately 0.252 N. However, when the angle is less than \(40^{\circ}\), the driving force increases rapidly to 2.634 N, due to the combined forces (\(F_{M1,3}+F_{M1,E}\)). Section A3 and B2 correspond to the maximum maintained hand stretching induced by driving current variations from \(-25\) to \(15\) A. Because the stretched finger angle is maintained, the acting force gradually decreases from 2.643 to 0.083 N according to the driving current, as shown in Figure 8c3. Thus, the applied negative current induced a combined force of \(F_{M1,3}+F_{M1,E}\), while the \(-25\)-A driving current generates a maximum force of 2.643 N. The applied positive current from 0 to 16 A induced an acting force of \(F_{M1,3}-F_{M1}\) and the applied current of 16 A generates a 0.083 N force. Section A4 shows the variations in force for  
Figure 8: (**a**) Trajectory of motion and Section A1 to A4, classified according to combination of M1, M2, and M3. (**b**) Trajectory of motion and the divided section from B1 to B3 without M2. (**c**) Variations in acting forces: (**c1**) and (**c2**) show the force acting in Section A1 and A2, respectively; (**c3**) shows the acting forces in Sections A3 and B2; (**c4**) shows the acting force in Section A4; (**c5**) and (**c6**) show the variations in the acting forces of Section B1 and B3, respectively. flexion from 16 to 25 A. In this case, when the finger angle reaches approximately 40\({}^{\circ}\), the driving force depends on \(F_{M1,E}\). At approximately 16 A, because the finger bends momentarily and shakes, the force distribution rapidly increases and decreases with angle changes from 0\({}^{\circ}\) to 40\({}^{\circ}\). In the angle range exceeding 40\({}^{\circ}\), the finger is stably bent, and the two forces (\(F_{M1,2}\) + \(F_{M1,E}\)) are added as the driving current increases, as shown in Figure 8c4. The force acting on the finger device under the maximum driving current reaches 0.764 N. Figure 8b shows the trajectory of motion and sections for the device without M2.