# Granular Media Friction Pad for Robot Shoes--Hexagon Patterning Enhances Friction on Wet Surfaces
## 2 Materials and Methods  
The granular media friction pad (GMFP) was composed of loose granular material that was encased by a thin, elastic membrane. The membrane was put flat on a lightweight, 3D-printed sample holder and clamped down using an adjusting washer (40 mm \(\times\) 50 mm \(\times\) 1 mm). Then, the granular material (1.7 ground coffee, Gold 100% Arabica, Markus Kaffee GmbH & Co., KG, Weyhe, Germany, see [1] for more details) was pushed behind the membrane through the lockable hole of the sample holder.  
Two different types of GMFP were investigated: one with a smooth membrane (see Figure 2a), and one with a hexagon-patterned membrane (see Figure 2b). The membranes, consisting of Dragon SkinTM 30 (Smooth-On, Inc., Macungie, PA 18062, USA) with a Young's Modulus of 0.53 \(\pm\) 0.02 MPa, were cast by pouring the uncured resin between two plastic foils, which were fixated on glass plates and separated by 1 mm spacers. This resulted in a 1 mm thick silicone membrane. For the hexagon membrane, a hexagon grid with 2.19 mm circumcircle, 0.4 mm groove width and 0.6 mm groove depth was 3D-printed from PLA using an Original Prusa 13 MK3 (Prusa Research s.r.o., Prague, Czech Republic). The grid was glued onto one of the plastic foils, before molding the membrane in the same way as the smooth membrane, so that the tops of the resulting hexagonal pillars had the same surface properties as the smooth membrane. There are three reasons for the selection of the hexagonal pattern: (1) As mentioned above, many biological systems use this evolutionarily optimized pattern for the purpose of grip enhancement on wet substrates [22; 25; 26; 36; 37; 38; 39]. (2) This pattern has been previously shown to enhance friction on substrates wetted by water [23; 27; 36; 37; 38]. (3) This pattern is relatively easy to design and adapt to curved substrates.  
Figure 2: GMFP and experimental setup. (**a**) Photograph of a GMFP with a smooth membrane, (**b**) photograph of a GMFP with a hexagonally patterned membrane; the membrane is cut open, showing the GMFP’s ground coffee filling, (**c**) schematic representation (left) and photograph (right) of the experimental setup.  
The GMFP fixed to the sample holder could slide freely on four vertical linear rods using low-friction linear bearings (see Figure 2c). The substrate, the flat side of wire mesh plywood (100 mm \(\times\) 100 mm), was pulled horizontally below the GMFP at 1 mm/s for 50 mm using a linear testing machine (Xforce HP 500 N, ZwickiLine, Zwick Roell, Ulm, Germany) that measured the pulling force. To obtain the sliding friction force, the pulling force was averaged for 10 s, 35 s after sliding started (see grey area in Figure 1c). To increase the normal load, \(F_{n}\), additional weights could be placed on top of the GMFP. The coefficient of friction, \(\mu\), was obtained as \(\mu=F_{fr}/F_{n}\).  
To examine the effect of membrane structuring on the friction performance of the GMFP under dry and lubricated conditions, both the smooth and the hexagon-patterned GMFP were produced 12 times and tested subsequently on a dry substrate and on an oily substrate. For the latter, mineral oil (Mineral oil 330779, Sigma-Aldrich Chemie GmbH, Tauftkirchen, Germany) was poured onto the substrate with a depth of at least 3 mm to fully submerge the contact area between the GMFP and substrate. For each sample and substrate combination, friction measurements were conducted at four different normal loads ranging from the sample weight itself (1 N) up to a maximum normal load of 19.36 N.