  Borrowing elementary ideas from solid mechanics and differential geometry,
this presentation shows that the volume swept by a regular solid undergoing a
wide class of volume-preserving deformations induces a rather natural metric
structure with well-defined and computable geodesics on its configuration
space. This general result applies to concrete classes of articulated objects
such as robot manipulators, and we demonstrate as a proof of concept the
computation of geodesic paths for a free flying rod and planar robotic arms as
well as their use in path planning with many obstacles.
