On the polar moment of inertia of the projection curve.
On the upward motion of a double cone on an inclined plane.
On the volume of the trajectory surfaces under the homothetic motions.
One parameter Lorentzian motions in Lorentz 3-space
Polkonfigurationen in der äquiformen Kinematik
Im allgemeinen ist die relative Momentanbewegung zweier komplanarer ähnlich-veränderlicher Systeme als Spiralung um einen aufzufassen (Abb. J.). Die bei drei Systemen auftretenden drei Pole bestimmen einen
Ponceletsche Dreieckscharen.
Príspevok k dôkazu Hartmannovej vety
Projective plane motions with infinitely many straight trajectories
The paper deals with one-parametric projective plane motins with the property that all points of the inflexion cubic have straight trajectories. It is shown that such motions have in the general case projective equivalent trajectories and that the inflexion cubic is in general irreducible. The cases of the above mentioned motions with reducible inflexion cubic are discussed in detail. The connection with the Darboux property is also mentioned.
Projective plane motions with straight trajectories
Properties of space motions with two straight trajectories
The paper is devoted to Euclidean space motions with two straight trajectories on two given skew straight lines. It describes all motions from this class which have one more planar trajectory in a plane not parallel to the given lines. In the conclusion it given conditions under which such motions have further planar trajectories in planes not parallel to the given skew straight lines.
Recent advances in the theory of holonomy
Robot-manipulators as submanifolds.
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).
Some Moebius-geometric theorems connected to Euclidean kinematics.
Special motions of robot-manipulators
There exist many examples of closed kinematical chains which have a freedom of motion, but there are very few systematical results in this direction. This paper is devoted to the systematical treatment of 4-parametric closed kinematical chains and we show that the so called Bennet’s mechanism is essentially the only 4-parametric closed kinematical chain which has the freedom of motion. According to [3] this question is connected with the problem of existence of asymptotic geodesic lines on robot-manipulators...
Spezielle äquiforme Zwangläufe
In der Ebene kann ein äquiformer Zwanglauf so bestimmt werden, daß jede Gerade einer beweglichen Ebene in einer festen Ebene eine zykloidale Kurve mit demselben Modul umhüllt. Das Problem wird ebenfalls im Raum gelöst und verallgemeinert.
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.
The development of the oloid.
The Euclidean plane kinematics
Restricting his considerations to the Euclidean plane, the author shows a method leading to the solution of the equivalence problem for all Lie groups of motions. Further, he presents all transitive one-parametric system of motions in the Euclidean plane.
The generalized Holditch theorem for the homothetic motions on the planar kinematics
W. Blaschke and H. R. Müller [4, p. 142] have given the following theorem as a generalization of the classic Holditch Theorem: Let be a 1-parameter closed planar Euclidean motion with the rotation number and the period . Under the motion , let two points , trace the curves and let be their orbit areas, respectively. If is the orbit area of the orbit curve of the point which is collinear with points and then In this paper, under the 1-parameter closed planar homothetic motion...