# Magnetically Deployable Robots Using Layered Lamina Emergent Mechanism
## 2 Materials and Methods
### Locomotion Mechanism  
The basic locomotion mechanism employed by the majority of the LEM prototypes in this paper is the friction-based stick-slip motion which relies on the induced magnetic torque from the APM to rotate the \"legs\" or \"flaps.\" Friction-based movements mimic the natural locomotion using properties such as frictional anisotropy [22; 39; 40], which can propel the object forward while preventing back-slippage [41]. The basic design of this mechanism includes the use of flaps located on the side that is in contact with the travelling surface. These flaps are attached with small permanent magnets (diameter 5 mm, thickness 1 mm ). When influenced by a magnetic field applied by a stronger and larger permanent magnet of size 25 mm \(\times\) 25 mm \(\times\) 25 mm, these small internal magnets will rotate, consequently inducing the flaps they are attached on to move in a fashion that propels the structure forward. As a proof of concept, a simple triangular prism design made of paper was fabricated to incorporate a base (21 mm \(\times\) 21 mm ) with trapezoidal flaps attached with IPMs (Figure 1a). Flaps of length 4 mm are cut into trapezoidal shapes based on their relatively more efficient performance in a pneumatic actuated kirigami snake paper [34]. Several magnetization direction combinations and magnet types were tested to compare and determine the characteristics of the movement (Figure 1b). The out-of-plane (OOP) direction represents the orthogonal direction with respect to the flap on which the magnet is placed, while the in-plane (IP) direction represents parallel magnetization with the flap. IPMs are attached to the flaps by either adhesive tape. These different placements of magnetization directions are tested and compared, as shown in Table 2.  
An alternative to attaching tiny rigid magnets to the flaps is to coat magnetorheological elastomer (MRE) onto the flaps. This approach also allows us to modify the strength and orientation of magnetization. Using MRE, we can fabricate various customizable domains that can create more versatile movements, allowing us to customize the material with non-uniform magnetization directions if needed. MRE sheets can be fabricated by mixing ecoflex (or polydimethylsiloxane) and neodymium powder in the ratio of 1:4 and letting the mixture cure. The fabricated sheet has soft, elastic properties and can be magnetized and set in the desired polarity by placing it in suitable configurations under the influence of a strong magnetic field. In general, thicker MRE sheets contain a greater density of magnetic particles and can provide greater magnetic torque when stimulated by the same external magnetic field, which helps to prop up the body and propel the mechanism more significantly than thinner MRE sheets. Table 2 compares the different combinations of magnet types and magnetization direction. As the flaps rotate and push the prism base up from the ground, we observe that the prism is vulnerable to flipping in response to the strong magnetic torque. Hence, anchoring using additional soft magnets on the base is required, as soft magnets are attracted to the APM regardless of its orientation. We chose to use IPMs instead of MRE sheets for the rest of the paper due to the stronger magnetic field interactions and ease of integration.