title: Correcting Duporcq's theorem.
abstract: In 1898, Ernest Duporcq stated a famous theorem about rigid-body motions with spherical trajectories, without giving a rigorous proof. Today, this theorem is again of interest, as it is strongly connected with the topic of self-motions of planar Stewart-Gough platforms. We discuss Duporcq's theorem from this point of view and demonstrate that it is not correct. Moreover, we also present a revised version of this theorem.
authors.affiliation: Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstrasse 8-10/104, Vienna A-1040, Austria.
authors.forename: Georg
authors.initials: G
authors.lastname: Nawratil
keywords: Architectural singularity; Borel Bricard problem; Self-motion; Stewart–Gough platform