  We propose a modified version of the Tomlinson model for static friction
between two chains of beads. We introduce disorder in terms of vacancies in the
chain, and distribute the remaining beads in a scale invariant way. For this we
utilize a generalized random Cantor set. We relate the static friction force,
to the overlap distribution of the chains, and discuss how the distribution of
the static friction force depends on the distribution of the remaining beads.
For the random Cantor set we find a scaled distribution which is independent on
the generation of the set.
