  We propose an explanation of the genesis of directional dry friction, as
emergent property of the oscillations produced in a bristle-like mediating
element by the interaction with microscale fluctuations on the surface.
Mathematically, we extend a convergence result by Mielke, for
Prandtl-Tomlinson-like systems, considering also non-homothetic scalings of a
wiggly potential. This allows us to apply the result to some simple mechanical
models, that exemplify the interaction of a bristle with a surface having small
fluctuations. We find that the resulting friction is the product of two
factors: a geometric one, depending on the bristle angle and on the fluctuation
profile, and a energetic one, proportional to the normal force exchanged
between the bristle-like element and the surface. Finally, we apply our result
to discuss the with the nap/against the nap asymmetry.
