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.

     

Orlicz spaces,spline systems,and brownian motion

There are three results proved in this paper. The first one characterizes the Hölder classes in Orlicz spaces by the coefficients of the orthogonal spline expansions of the Franklin type. The second one gives a sharp estimate for the correlation of two random variables obtained as a composition of two Borel functions with the components of a given two-dimensional Gaussian vector. The third one is obtained with the help of the first two and it states that the Wiener measure is concentrated on the Banach space of Hölder functions with exponent 1/2 but in the norm of the Orlicz spaceL _M ^* withM(t)=expt(t ²)?1.     

Quinaldine derivatives with fluorine-containing substituents and cyanine dyes based on them

Condensation of fluorine-containing anilines with paraldehyde gave quinaldine derivatives with CF₃, CF₃S, and CF₃SO₂ groups in the 6 position, from which carbocyanine, merocyanine, and styryl dyes were synthesized. Fluorine-containing groups lower the basicity of quinaldine by 0.7–2.0 pK_a units and lead to deepening of the color of the dyes.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 76–78, January, 1978.     

Unusual coordination of the in(3+) atom in the decahydrated complex Na3{In[N(CH2COO)3]2}·9H2O

All-Union Scientific-Research Institute of Chemical Reagents and Ultrapure Chemical Substances. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 2, pp. 163–166, March–April, 1991.     

Synthesis and some properties ofN-polynitromethyl derivatives of fused benzotriazoles

The procedures for the synthesis ofN-polynitromethyl derivatives of benzo[1,2-d;4,5d]ditriazole-4,8-dione are described. Some chemical properties of the compounds obtained are investigated.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1623–1625, September, 1993.