# Magnetically Deployable Robots Using Layered Lamina Emergent Mechanism
## 2 Materials and Methods
### Lamina Emergent Mechanism  
Lamina Emergent Mechanisms (LEMs) are mechanisms designed from planar material capable of out-of-plane motions. LEM can be advantageous in carrying out complicated mechanical tasks in constrained environments due to its compact design [42]. Using this concept and the crawling mechanism mentioned above, a design was created that involves pairs of legs (attached with IPMs) coupled with one another that can rotate simultaneously out of the lamina plane. Additional anchoring is provided with a soft magnet at the rear end of the LEM to prevent flipping and provide more stable forward locomotion. Each pair of legs has a size of 14 mm \(\times\) 21 mm (L \(\times\) W), leg length of 10 mm, leg width of 7 mm, and foot-to-foot spacing of 21 mm. The prototype of a single layer of LEM (SLEM) is shown in Figure 2 (dimensions 65 mm \(\times\) 35 mm ). We used 300 gsm paper to fabricate the structure body. As the stiffness of the paper tends to reduce the range of motion of its legs, we create partial cuts in the mountains or valleys folds of the crease pattern of the design [43; 44] (Figure 2). The partial cut is placed on every the \"mountain\" edge of every fold to reduce restriction in folding. However, we observed that the basic movement produced by the SLEM is still susceptible to flipping and backward slippage and has a limited locomotion style. Hence, we considered other designs of the SLEM structure. The next LEM structure, named Dual-Layer LEM (DLLEM), comprises two identical SLEM structures (Figure 3). Two sheets are pasted in an orientation that mirrors the other. We test the ability of the structure to crawl in a more confined environment (height 16 mm ) where the robot can use both sides to create friction-based movement (Figure 3b). This DLLEM structure is also made of 300 gsm paper and has its feet and \"spine\" (the central part that connects all pairs of legs) reinforced by plastic sheets to reduce wear and tear. Two pairs of small neodymium disc magnets are attached to two different pairs of legs, each on one side of the structure. This way, both pairs of magnets can simultaneously rotate and pop up the structure's legs at the same time when a magnetic field is applied. The structure is placed between two styrofoam sheets to mimic surrounding frictional surfaces that can also prevent flipping or rotation of the body. Limitations of this mechanism include stability and the ability to only crawl in more confined environments. Given that the robot moves based on the simultaneous rotation of parallel pairs of legs (coupling), it affects the independent motion of each pair of legs. This may limit the dynamic freedom of each leg during motion and, therefore, might be less flexible and unable to overcome obstacles and traverse more challenging terrains. Figure 2: SLEM: (**a**) Top–down view of SLEM base with mountain and valley folds represented by dotted lines, cuts represented by continuous black lines (leg length 10 mm ). IPMs (black circles) are attached to the front legs, and soft magnet stripes attach to the tail for increased anchoring (leg length 10 mm ). (**b**) Three-dimensional (3D) simulation of SLEM in the pop-up configuration (leg length 14 mm ). When the SLEM is under the influence of a magnetic field, the legs pop up, thus pushing the SLEM body/base upward and forward (leg length 10 mm ). To overcome the limitations observed in the DDLEM design, we modified the LEM by assembling two layers of SLEM per side (for a total of four SLEM sheets) as shown in Figure 4. The dimensions of certain parts of the SLEM design were modified to fit one SLEM sheet inside the other to act as opposite-moving pairs of legs. We name the mechanism Alternating Mirror Direction LEM (AMDLEM) due to the opposite mirror direction in which the structure legs on one SLEM sheet move with respect to those on the other SLEM. To achieve directional movement, legs with fixed directions are added to the AMDLEM to allow greater backward friction and easier forward slip.