## 3 Results  
### Serpentine Architecture  
One solution that addresses the weave's problems, as outlined in the Section 1 is the serpentine architecture (Figure 1). It is named \"serpentine\" due to the snake-like winding of the microchannels. Figure 1A shows an isometric view and Figure 1B shows a side view of \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & \multicolumn{10}{c}{_Size (Channel)_} \\ \hline  & \multicolumn{3}{c}{**XL**} & \multicolumn{3}{c}{**L**} & \multicolumn{3}{c}{**S**} & \multicolumn{3}{c}{**XS**} \\ \hline
**Chip ID** & 1 & 2 & 3 & 1 & 2 & 3 & 1 & 2 & 3 & 1 & 2 & 3 \\ \hline
**1** & 100 & 100 & 100 & 100 & 100 & 100 & 34.3 & 11.9 & 0 & 0 & 0 & 0 & 0 \\ \hline
**2** & 100 & 100 & 100 & 100 & 100 & 100 & 100 & 100 & 100 & 32.9 & 16.3 & 6 \\ \hline
**3** & 100 & 100 & 100 & 100 & 100 & 100 & 39.9 & 83.7 & 0.1 & 0.1 & 0.1 \\ \hline
**4** & 100 & 100 & 100 & 100 & 100 & 100 & 100 & 100 & 77.3 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Clearance of single-serpentine channels by channel size. All values represent the percentage of the channel arclength that was successfully cleared. Figure 1: The serpentine artificial muscle fiber architecture is formed of two entwining microchannels shown in light and dark gray, respectively. These microchannels have a constant cross-section and thus offer improved manufacturability. (**A**) Isometric view. (**B**) Side view. (**C**) Single-serpentine arrays were super-arrayed inside 3D-printed chips (1–4) and subjected to the support material clearing procedure [59]. The approximate chip size was 41 mm \(\times\) 53 mm (width \(\times\) length). See Table 2 for the quantitative results. (**D**) Double-serpentine chips whose microchannels were printed and filled with black resin to improve optical contrast for visualization. the geometry. Each serpentine is a single channel with an essentially constant cross-section along the length of the channel. This avoids the weave's bottlenecks, which can produce clogging and interfere with the clearance process. Also, there are no dead-end corners as in the weave, which would be difficult to clear due to reduced flow speed. Like the weave, the serpentine can be axially extended as desired by repeating the pattern as many times as needed. Furthermore, as only the individual fiber element of the weave is directly replaced, the overarching connecting structures, such as the dendritic tree structures in the lateral dimensions, remain the same. Hence the serpentine structure addresses several implementation issues compared to the weave structure while still benefiting from the advantages of the microchannel branching introduced with the weave [33]. The serpentine is designed in such a way that the distance between the parts of the channels that make up the microcapacitor plates is at least three times smaller than the distance between the channels in the lateral direction of the fiber. Hence, the force produced in the intended longitudinal contraction [36] is at least 9 times larger compared to an unintended lateral contraction. That lateral contractive force can limit lateral expansion, which hinders the desired longitudinal contraction. The bounded geometric ratio should help minimize this effect and, thus, should improve the overall performance of the muscle. With channel cross-sections in the order of hundreds of micrometers and microcapacitor separation in the order of tens of micrometers, FEA simulations have indicated that hundreds of kPa of force density can be produced [36; 58], while experimental characterizations have proven that the 3D-printed microchannels can be appropriately formed and cleared [59; 60]. The serpentine architecture was implemented in test chips fabricated in soft resin using the now established 3D-printed microfluidics technique, including embedded channels and a support material clearance procedure [59; 60; 64].