Geodesic
On Equiform Stewart Gough Platforms with Self-motions
Journal for geometry and graphics, Tome 17 (2013) no. 2, pp. 163-175 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 53A17, 68T40
Mots-clés : Stewart Gough platform, self-motion, bond theory, cylinder of revolution 
@article{JGG_2013_17_2_JGG_2013_17_2_a3,
     author = {G. Nawratil },
     title = {On {Equiform} {Stewart} {Gough} {Platforms} with {Self-motions}},
     journal = {Journal for geometry and graphics},
     pages = {163--175},
     year = {2013},
     volume = {17},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2013_17_2_JGG_2013_17_2_a3/}
}
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G. Nawratil . On Equiform Stewart Gough Platforms with Self-motions. Journal for geometry and graphics, Tome 17 (2013) no. 2, pp. 163-175. http://geodesic.mathdoc.fr/item/JGG_2013_17_2_JGG_2013_17_2_a3/