# Magnetically Deployable Robots Using Layered Lamina Emergent Mechanism
## 4 Discussion
### Effect of Leg Length  
As longer leg lengths can potentially propel the structure body further forward, testing was carried out to determine the effects of LEM leg length on its movement (Figure 16). An SLEM design with a leg length of 20 mm (named SLEM-20) is created to compare against the original 10 mm SLEM leg length (named SLEM-10). A force sensor F/T Sensor: Nano17 (ATI Industrial Automation) is attached to the SLEMs via a copper string. When the structure moves forward, it pulls on the string, and the force values are recorded in the ATI software. Propulsion forces are measured, and the average peak force was calculated for the two different types of structure base materials (300 gsm paper vs. 70 gsm paper), two different leg lengths (20 mm vs. 10 mm ) and measured at two different points on the structure (tail vs. leg), as summarized in Table 6.  
Table 6 shows that the propulsion force measured at the tail is generally lower than that at the leg, as the leg is the main actuated component of the structure. Using thinner materials to fabricate the LEM results in more flexibility and therefore a larger range of motion, allowing for slightly greater propulsion force. The SLEM-20 is shown to generate greater propulsion force. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Time Taken to** & **No. of Cycles** & **Speed (mm/s)** & **Stride Length (mm)** \\ \hline Paper & 16.1 & 8 & 9.32 & 18.75 \\ \hline Foam & 14.9 & 7 & 10.07 & 21.43 \\ \hline Bubble wrap & 22.4 & 11 & 6.70 & 13.64 \\ \hline Towel (woven cotton) & 20.7 & 9 & 7.25 & 16.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Speed of SLEM on different frictional surfaces. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Surface**} & **Angle Forward** & **Angle Backward** & \multicolumn{3}{c}{**Coefficient of Friction**} \\ \cline{3-5}  & & \multicolumn{2}{c}{**Forward Friction \(\mu_{\text{f}}\)**} & **Backward Friction \(\mu_{\text{b}}\)** \\ \hline Paper & 22.4 & 27.9 & 0.41 & 0.53 \\ \hline Foam & 37.6 & 40.3 & 0.77 & 0.85 \\ \hline Bubble wrap & 70.2 & 85.4 & 2.78 & 12.43 \\ \hline Towel (woven cotton) & 59.5 & 71.3 & 1.70 & 2.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Coefficient of friction between the AMDLEM and different frictional surfaces. Figure 17 shows the propulsion force measured for the repeated movement of the SLEM when it is in its normal upright position and secured onto the horizontal plane upside down. The upside-down SLEM is taped to the horizontal platform with its leg attached to the sensor. Hence, the force measured is more stable and solely as a result of magnetic actuation. It does not have to account for balancing and propelling the SLEM forward. We observed that the propulsion force generated by the SLEM-10 is generally higher than the force generated by SLEM-20. This could be explained by the closer distance of the IPM to the APM on the 10 mm leg when upside down compared to that on the 20 mm leg. There are a total of 18 cycles completed within 25 s by the SLEM-10, which is 1.8 times greater than the 10 cycles completed by the SLEM-20. The faster rotation also results in higher acceleration, thus resulting in a higher pulling force on the sensor. In Figure 17 we can see that the propulsion force peaks at 0.28 N for the SLEM-20 compared to 0.20 N for the SLEM-10. However, due to the greater leg length, the movement is much more unstable, as seen in the greater fluctuation of propulsion force by the 20 mm leg. The shorter leg length of 10 mm provides more stable and consistent propulsion forces with higher rotation frequency. Hence, we conclude that the higher the leg length, the further the IPMs are away from the APM, which leads to a lower controllability and stability of the structure, despite the potentially higher propulsion force and stride length.