Flexible Octahedra in the Projective Extension of the Euclidean 3-Space
Journal for geometry and graphics, Tome 14 (2010) no. 2, pp. 147-169
Cet article a éte moissonné depuis la source Heldermann Verlag
We complete the classification of flexible octahedra in the projective extension of the Euclidean 3-space. If all vertices are Euclidean points then we get the well known Bricard octahedra. All flexible octahedra with one vertex on the plane at infinity were already determined by the author in the context of self-motions of TSSM manipulators with two parallel rotary axes. Therefore we are only interested in those cases where at least two vertices are ideal points. Our approach is based on Kokotsakis meshes and reducible compositions of two four-bar linkages.
Classification :
53A17, 52B10
Mots-clés : Flexible octahedra, Kokotsakis meshes, Bricard octahedra
Mots-clés : Flexible octahedra, Kokotsakis meshes, Bricard octahedra
@article{JGG_2010_14_2_JGG_2010_14_2_a2,
author = {G. Nawratil },
title = {Flexible {Octahedra} in the {Projective} {Extension} of the {Euclidean} {3-Space}},
journal = {Journal for geometry and graphics},
pages = {147--169},
year = {2010},
volume = {14},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JGG_2010_14_2_JGG_2010_14_2_a2/}
}
G. Nawratil . Flexible Octahedra in the Projective Extension of the Euclidean 3-Space. Journal for geometry and graphics, Tome 14 (2010) no. 2, pp. 147-169. http://geodesic.mathdoc.fr/item/JGG_2010_14_2_JGG_2010_14_2_a2/