  The main purpose of this paper is to investigate commuting flows and
integrable systems on the configuration spaces of planar linkages. Our study
leads to the definition of a natural volume form on each configuration space of
planar linkages, the notion of cross products of integrable systems, and also
the notion of multi-Nambu integrable systems. The first integrals of our
systems are functions of Bott-Morse type, which may be used to study the
topology of configuration spaces.
  Dedicated to Anatoly T. Fomenko on the occasion of his 75th birthday
