On two methods of determining the ellipses and ellipsoids of positioning accuracy of robot manipulators

Summary When analysing the problem of the positioning accuracy of robot manipulators it is important to know how far random deviations of the hand may be from the desired position if the joint positioning errors possess a normal distribution. Two methods of determining the ellipses and ellipsoids of probability concentration are compared. The first of them is based on the standard procedure of the probability calculus. The second approximate method consists in finding at first the polygon or polyhedron of the positioning accuracy, and then in finding the ellipse or ellipsoid with principal axes and second order moments coinciding with those of the polygon or polyhedron, respectively. Examples of application demonstrate that these two methods give very close results.

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Zwei Methoden zur Bestimmung der Ellipsen und Ellipsoide der Positioniergenauigkeit von Handhabungsrobotern

Übersicht Bei der Untersuchung der Positioniergenauigkeit von Handhabungsrobotern ist es wichtig, die Größe zufälliger Abweichungen des Greifers von der erstrebten Position zu kennen, wenn die Lagefehler der Verbindungen eine Normalverteilung besitzen. Es werden zwei Methoden zur Bestimmung der Ellipsen bzw. Ellipsoide der Wahrscheinlichkeitsdichte verglichen. Die erste beruht auf dem Standardverfahren der Wahrscheinlichkeitsrechnung. Die zweite Näherungsmethode besteht darin, daß zunächst das Polygon bzw. Polyeder der Positioniergenauigkeit bestimmt wird und danach die Ellipse bzw. das Ellipsoid mit den Hauptachsen und Momenten zweiter Ordnung wie das Polygon oder Polyeder. Beispiele zeigen, daß beide Methoden zu sehr ähnlichen Ergebnissen führen.

     

Condensed matter effects on nuclear fusion rates in laboratory and astrophysical environments

Previously overlooked condensed matter effects (CME) can significantly influence nuclear fusion rates in both laboratory and astrophysical environments. In dense plasmas, the ensemble of fusing particles has a significant exchange of kinetic and potential energies. Thus, there are diminished effective flux velocities resulting in a significant selective reduction of fusion rates. Our CME predictions are testable in laboratory experiments and have broad-ranging implications on the fusion rates for stellar media in general. By calculating reaction rates forp(p, e ⁺ v _e ) D and⁷Be(p, )⁸B in the sun, we show that CME help to solve the solar neutrino problem.     

Zirconocene-mediated route to enantiopure 9-oxabicyclononanes functionalized on both carbon bridges

[reaction: see text] A zirconocene-mediated ring contraction of 4-vinylfuranosides generated either from d-arabinose or d-glucose is followed by sequential oxidation to the ketone and alkynyl Grignard addition. The resulting cis-cyclobutanediols are subjected in turn to thermal rearrangement and intramolecular oxymercuration-demercuration. The regiochemistry of the final ring closure is controlled by the nature of R.     

Struktur von 7,11-Diphenyl-2,4-diazaspiro[5,5]undecan-1,3,5,9-tetraonen durch LIS-NMR

A semi-quantitative method for determining distances between a possible coordination centre and protons from LIS-NMR values is developed for the title compounds3, although these have four coordination points. This makes it possible to propose structures and conformations for the isomers of3.

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Mit 4 Abbildungen

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H.-H. Otto undH. Yamamura, Ann. Chem., im Druck.