Speaker: Hans-Christian Graf v. Bothmer (Hamburg)
Title: Movable Hexapods
Abstract: In 1904 the French Academy of Science posed the
following (still unsolved) question for the Prix Vaillant
Determine and study all displacements of a rigid body in which
distinct points of the body
move on spherical paths
An interesting class of such mechanisms are so called n-pods.
These are mechanical devices constituted of two rigid bodies, the
base and the platform, connected by n other rigid bodies, called
legs, that are anchored via spherical joints (see picture).
The question is how to arrange the legs such that the platform can
move while the base is fixed. In this case the pod is called
"movable". The first nontrivial family of movable n-pods was found by
Borel also in 1904.
For dimension reasons the case n=6 (hexapods) is the most interesting.
Even the classification of movable hexapods is still open today - as
recently as 2015 a completely new family was found by Matheo Gallet,
Georg Nawratil and Joseph Schicho.
In this talk I will explain how this problem can be formulated in
algebraic geometry and present the results of a computer experiment
that gives a heuristic overview of the parameter space of all movable