Integrable systems in planar robotics

Abstract

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.