Journal for Geometry and Graphics 16 (2012), No. 2, 139--151
Copyright Heldermann Verlag 2012
Necessary Conditions for Type II DM Self-motions of Planar Stewart Gough Platforms
Georg Nawratil
Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstr. 8-10/104, 1040 Vienna, Austria
nawratil@geometrie.tuwien.ac.at
Due to a previous publication of the author, it is already known that one-parametric self-motions of Stewart Gough platforms with planar base and planar platform can be classified into two so-called Darboux Mannheim (DM) types (I and II). Moreover, the author also presented a method for computing the set of equations yielding a type II DM self-motion explicitly. Based on these equations we prove in this article the necessity of three conditions for obtaining a type II DM self-motion. Finally, we give a geometric interpretation of these conditions, which also identifies a property of line-symmetric Bricard octahedra, which was not known until now.
Keywords: Self-motion, Stewart Gough platform, Borel Bricard problem, Bricard octahedra.
MSC: 53A17; 52B10
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