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Journal for Geometry and Graphics 17 (2013), No. 2, 163--175
Copyright Heldermann Verlag 2013

On Equiform Stewart Gough Platforms with Self-motions

Georg Nawratil
Institute of Discrete Mathematics and Geometry, University of Technology, Wiedner Hauptstr. 8-10/104, 1040 Wien, Austria

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 self-motions, if they are architecturally singular; i.e., the anchor points are located on a conic section. Therefore this study focuses on the non-planar case. We prove that an equiform SG manipulator has translational self-motions, if and only if it is a so-called reflection-congruent one. Moreover we give a necessary geometric property of non-planar equiform SG platforms for possessing non-translational self-motions by means of bond theory. We close the paper by discussing some non-planar equiform SG platforms with non-translational self-motions, where also a set of new examples is presented.

Keywords: Stewart Gough platform, self-motion, bond theory, cylinder of revolution.

MSC: 53A17; 68T40

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