Classical geometry and computers.
Robot-manipulators as submanifolds.
3D-Darboux motions in 4-dimensional Euclidean space.
Curvature Properties of 6-Parametric robot manipulators.
Geometry of the Motion of Robot manipulators.
Kinematic geometry in -dimensional Euclidean and spherical space
Darboux motions in
Kinematic geometry of regular motions in homogeneous space
Equiaffine Darboux motions with double roots
Affine Darboux motions
Kinematická geometrie grupy euklidovských podobností v rovině
Poznámka k definici Kleinovy kvadriky v metrické přímkové geometrii
Axiody obecného afinního pohybu
Affine space motions with only plane trajectories
Lieovy grupy a kinematická geometrie v rovině
Grundlagen der räumlichen kinematischen Geometrie. I.
Im Artikel sind mit Hilfe der Lieschen Gruppen und Algebren die Eigenschaften und Invarianten der räumlichen Bewegung gefunden.
Grundlagen der räumlichen kinematischen Geometrie. II
Der Artikel ist eine Vorsetzung des ersten Teiles des Artikels und ist der Analyse und der Synthese der helikoidalen Bewegungen gewidmet. Im der Analyse der helikoidalen Bewegungen gewidmeten Teil sind die helikoidale Bewegungen als die Zweischraubenbewegungen charakterisiert und es sind die Invarianten der helikoidalen Bewegungen gefunden. Im, der Synthese der helikoidalen Bewegungen gewiemeten, Teil sind alle helikoidalen Bewegungen, die eine ebene oder gerade oder sphärische Punkttrajektorie...
The Darboux theorem on plane trajectories of two-parametric space motions
The paper contains the proof of the classification theorem for two-parametric space motions with at least 5 points with plane trajectories. The proof is based on [1] and on the cannonical form of a certain tensor of order 3. The second part of the paper deals with the problem of plane trajectories from the differential-geometrical point of view. Some applications are given.
Similarity motions in with plane trajectories
In this paper the author finds and describes all similarity space motions, which have only plane trajectories of points. All such motions are explicitly expressed. They are of 5 types, all of them cylindrical. Trajectories are conic sections (3 types) or arbitrary plane curves (2 types).
Euclidean space motions with affinely equivalent trajectories
The author studies the Euclidean space motions with the property that the trajectory of every point is an affine image of a given space curve. Such motions split into plane motions and translations and their trajectories are cylindrical curves. They are characterized as motions with the following property: Not all trajectories are plane curves and if any trajectory has a planar point, it lies in a plane. Motions with infinitely many straight trajectories form a special subclass of those motions....
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