2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33322It has recently been shown that any simple (i.e. nonintersecting) polygonal chain in the plane can be reconfigured to lie on a straight line, and any simple polygon can be reconfigured to be convex. This result cannot be extended to tree linkages: we show that there are trees with two simple configurations that are not connected by a motion that preserves simplicity throughout the motion. Indeed, we prove that an $N$-link tree can have $2^{Ω(N)}$ equivalence classes of configurations.16 pages, 6 figures Introduction reworked and references added, as the main open problem was recently closedComputational GeometryDiscrete MathematicsF2.2text