
Journal for Geometry and Graphics 17 (2013), No. 2, 163175 Copyright Heldermann Verlag 2013 On Equiform Stewart Gough Platforms with Selfmotions Georg Nawratil Institute of Discrete Mathematics and Geometry, University of Technology, Wiedner Hauptstr. 810/104, 1040 Wien, Austria nawratil@geometrie.tuwien.ac.at A Stewart Gough (SG) manipulator, where the platform is similar to the base, is called equiform SG manipulator. It is well known that these SG manipulators with planar platform and planar base only have selfmotions, if they are architecturally singular; i.e., the anchor points are located on a conic section. Therefore this study focuses on the nonplanar case. We prove that an equiform SG manipulator has translational selfmotions, if and only if it is a socalled reflectioncongruent one. Moreover we give a necessary geometric property of nonplanar equiform SG platforms for possessing nontranslational selfmotions by means of bond theory. We close the paper by discussing some nonplanar equiform SG platforms with nontranslational selfmotions, where also a set of new examples is presented. Keywords: Stewart Gough platform, selfmotion, bond theory, cylinder of revolution. MSC: 53A17; 68T40 [ Fulltextpdf (256 KB)] for subscribers only. 