# Magnetically Deployable Robots Using Layered Lamina Emergent Mechanism
## 3 Results
### Relationship between Leg Locomotion and Actuating Magnet  
A movement cycle can be split into six phases, as seen in Figure 6, in which the purple arrows indicate the direction of magnetization of the mechanism flaps, and the black arrows indicate the direction of rotation. Firstly, the trapezoidal flaps on the mechanism remain in-plane with respect to the mechanism's base. When the APM rotates clockwise, it exerts a magnetic torque that repels the IPM on the flaps, causing the flaps to rotate anticlockwise and become vertical at phase 3. When the APM continue to rotate beyond 90\({}^{\circ}\), the rotation of the flap extends to more than 90\({}^{\circ}\) with respect to the horizontal plane. The maximum rotation angle is achieved in phase 4, providing an optimum contact point and acting as a hinge for the forward  
Figure 5: Using magnetometer to measure magnetic field strength. (**a**) The magnetometer sensor tip is placed on the testing surface with the actuating permanent magnet placed right below it and the SLEM structure right on top. (**b**) Magnetic field strength, rotation angle \(\theta\) of magnetic field, and vertical distance of APM from sensor versus time. Rotation angle \(\theta\) is measured regarding the direction of the magnetic field with respect to the vertical direction. The rotation occurs anticlockwise, and once the magnet and magnetic field are completely inverted (by 180\({}^{\circ}\)), the magnet is rotated clockwise to revert to its original position. (**c**) Magnetic field strength plotted against rotation angle of magnetic field for one cycle. propelling motion in phases 5 and 6. Displacement will be seen in phases 5 and 6. Figure 6b represents the sinusoidal rotation of the actuating magnet in terms of y-coordinates, which takes approximately 14 s to complete nine cycles. [PERSON] [46] developed an origami simulator to simulate the folding of the designs presented in this paper, where the strain visualization was generated by adjusting the folding parameters. Designs follow the predetermined set of rules by the simulator, where certain line colors and line opacity indicate the direction of folds (valley and mountain) and the extent of folding (opacity), respectively. The parameters defined were axial stiffness, face stiffness, fold stiffness, facet crease stiffness, damping ratio, and maximum strain level allowed by the material. Figure 7 shows the strain visualization of the base design of the triangular prism mechanism when the flaps rotate outward. The parameters are set at maximum, with the maximum strain level set at 1%. Due to the simple arrangement of the creases on the design, the folds are easily achieved and do not result in significant strain. Strain analysis was also carried out on the base design of the LEM mechanism. Figure 8 shows that increasing the facet crease stiffness results in increased structural rigidity and strength of the material and a decrease in the strain level at the joints. Parameter values  
Figure 6: Locomotion mechanism presented in this paper: (**a**) Basic locomotion mechanism using an APM, split into six phases. The mechanism base has trapezoidal flaps attached with internal permanent magnets (IPM) with the direction of magnetization indicated by the purple arrows. Rotation of APM triggers the IPM (and consequently the trapezoidal flaps) to rotate, propelling the mechanism forward. (**b**) Sinusoidal representation of the movement of actuating magnet at approximately 0.6 Hz. (**c**) Magnetic field strength B (mT) of APM measured against rotation angle of the APM, in which the rotation angle is set to be the vertical direction with the north pole facing the sensor. used in the simulator remain constant: max strain value 5%, maximum axial stiffness, face stiffness, fold stiffness, and damping ratio. The facet crease stiffness results are adjusted to the following values: (a) 0.2, (b) 1, (c) 3 (maximum value).