ABSTRACT: Consider a planar linkage, a polygonal arc consisting of
rigid bars joined at incident endpoints, in other words, a
polygonal chain.  (This is the ruler that a carpenter folds
up in a pocket.) We prove that the linkage can be
continuously moved so that the arc become straight and no
bars cross while preserving the bar lengths. Furthermore,
our motion is piecewise-differentiable, does not decrease
the distance between any pair of vertices, and preserves any
symmetry present in the initial configuration. The problem
has a long history and several people have worked on this
and related problems.  This is joint work with Erik Demaine
and Guenter Rote.