Reasoning on linkages

By Tomás Recio, Zoltán Kovács and M. Pilar Vélez. We describe some on-going work on the crossroad of mechanical linkages, dynamic geometry and automatic reasoning tools. In particular, we shall consider how these new tools can be used for linkage exploration, i.e. for the automatic derivation of the locus equation for some relevant moving point in a linkage (e.g. linkages for generating specific algebraic curves, such as Peaucellier's construction of a straight line), and, in this way, for the verification (automatic proving) of the correctness of the linkage construction, as well as, for finding (automatic discovery) a suitable modfiication on a given linkage for achieving a desired movement.