Geodesic
Necessary Conditions for Type II DM Self-motions of Planar Stewart Gough Platforms
Journal for geometry and graphics, Tome 16 (2012) no. 2, pp. 139-151.

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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.
Classification : 53A17, 52B10
Mots-clés : Self-motion, Stewart Gough platform, Borel Bricard problem, Bricard octahedra 
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     title = {Necessary {Conditions} for {Type} {II} {DM} {Self-motions} of {Planar} {Stewart} {Gough} {Platforms}},
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G. Nawratil . Necessary Conditions for Type II DM Self-motions of Planar Stewart Gough Platforms. Journal for geometry and graphics, Tome 16 (2012) no. 2, pp. 139-151. http://geodesic.mathdoc.fr/item/JGG_2012_16_2_JGG_2012_16_2_a2/