  We study the equations of overdamped motion of an inextensible triod with
three fixed ends and a free junction under the action of gravity. The problem
can be expressed as a system of PDE that involves unknown Lagrange multipliers
and non-standard boundary conditions related to the freely moving junction. It
can also be formally interpreted as a gradient flow of the potential energy on
a certain submanifold of the Otto-Wasserstein space of probability measures. We
prove global existence of generalized solutions to this problem.
