A Note on Reconfiguring Tree Linkages: Trees can Lock

Article dans revue scientifique avec comité de lecture.It has recently been shown that any polygonal chain in the plane can be reconfigured to lie on a straight line, and any polygon can be reconfigured to be convex. This result cannot be extended to tree linkages: we show that there are trees with two configurations that are not connected by a motion. Indeed, we prove that an $N$-link tree can have $2^{Omega(N)}$ equivalence classes of configurations