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.

     

Algebraic version of extension theory for a quantum system with internal structure

An explicit two-channel matrix representation is obtained for the Hamiltonians of systems with internal structure in the framework of the theory of extensions of symmetric operators. Generalized potentials that are equivalent to zero-range interactions with internal structure and automatically reproduce the boundary conditions that correspond to them asx0 are constructed.St. Petersburg State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 2, pp. 163–181, November, 1993.     

A note on the illumination of convex bodies

LetKE ^d be a convex body and letl _r(K) denote the minimum number ofr-dimensional affine subspaces ofE ^d lying outsideK with which it is possible to illuminateK, where 0rd–1. We give a new proof of the theorem thatl _r(K)(d+1)/(r+1) with equality for smoothK.The work was supported by Hung. Nat. Found. for Sci . Research No. 326-0213 and 326-0113.     

Reaction-diffusion model for combustion with fuel consumption: II. Robin boundary conditions

A model, derived in a previous paper, for the reaction betweena gaseous oxidant and a solid porous fuel is analysed furtherfor general Robin boundary conditions. Numerical solutions areobtained and the effects of varying the dimensionless parameters,particularly the Frank-Kamenetskii parameter and the Lewisnumber L, are discussed in detail and compared with resultsobtained previously when Dirichlet boundary conditions are applied.Analytic solutions are obtained for the small-time developmentand for large values of . This latter solution shows the existenceof a propagating reaction-diffusion burning wave, and has featureswhich are qualitatively different to those derived earlier.     

Matching the Kerr solution on the surface of a rotating perfect fluid

We investigate the possible shapes of the surface of a rigidly rotating perfect fluid on which is matched the Kerr metric, using the Boyer (1965) surface condition. The solution, given in Figures 1 to 5, depends on three parameters, = qK, q = a/m, - (a/gwc), wherem denotes the mass of the source, a its angular momentum per unit mass, the angular velocity of rotation, andK is an integration constant appearing in Boyer's surface condition. When < 1, as in Figures 1 to 3, there are, for givenq and, two possible surfaces, of which the smaller one touches the ring-singularity at = a, z = 0. When > 1, as in Figures 4 and 5, there is only one possible surface of kidney-shaped tori, which also touch the ring singularity. In the case of a differentially rotating perfect fluid, we find a variety of possible strictly spheroidal surfaces, depending on the choice of an arbitrary integration function() of the angular velocity . If we choose() so that, at each point on the surface, is single-valued, then the resulting distribution exhibits an equatorial acceleration, similar to what is observed on the surface of the sun. This angular velocity distribution turns out to be identical with Thorne's (1971) angular velocity of cumulative dragging.     

Synthesis of polypyromellitimidoamides from dihydrazides of aromatic and aliphatic acids and pyromellitic dianhydride

Polyamido acids have been synthesized from pyromellitic dianhydride and dihydrazides of terephthalic, isophthalic, sebacic, and adipic acids. The polyamido acids obtained have been cyclized at 220° C, and it has been shown by IR spectroscopy that the polymers contain five-membered imide rings.     

Technetium-99m-diethyl-IDA instant kit: Labelling kinetics and biological properties

A formulation of stannous-diethyl-IDA freeze-dried kit, containing 50 mg diethyl-IDA and 0.4 mg hydrated stannous chloride, to be labelled with technetium has been developed for hepatobiliary scintigraphy. Gel chromatography column scanning technique has been applied for determination of technetium fractions in the preapration. The optimal pH value of the preparation with a high hepatobiliary specificity was found between 5.5 to 6.0. Effect of ligand to metal ratio on the stability of the prepared Sn-diethyl-IDA solution prior mixing with technetium has been investigated. The reaction conditions (initial pH) between the ligand and stannous ion affects the percent hydrolysis of the labelled compund, i.e. the formation rate of the complex. The organ distribution data of^99mTc-diethyl-IDA in mice for 60 minutes post injection were satisfactory. The radiopharmaceutical exhibits rapid blood clearance, great hepatic clearance and very short hepatocyte transit time. Uptake of the radiopharmaceutical in various organs of mouse at 5 minute post injection showed that the greater part of the injected radioactivity has distributed between liver and intestine. However, about 12% and 60% of the injected dose has been found in liver and intestine respectively. The renal uptake of the HB agent in mice is relatively low and decreases with time to become about 0.3% at 60 minutes post injection. Blood clearance data of the radiopharmaceutical kit in rabbits showed that the HB agent is-rapidly cleared, since the initial decrease was very fast with a half-time of 1.5 minutes.