Reference Circle Research Articles

A stochastic optimization approach for roundness measurements

In this paper, we develop a vision-based inspection system for roundness measurements. A stochastic optimization approach has been proposed to compute the reference circles of MIC (maximum inscribing circle), MCC (minimum circumscribing circle) and MZC (minimum zone circle) methods. The proposed algorithm is a hybrid optimization method based on simulated annealing and Hooke–Jeeves pattern search. From the experimental results, it is noted that the algorithm can solve the roundness assessment problems effectively and efficiently. The developed vision-based inspection system can be an on-line tool for the measurement of circular components.

Characterisation of spatial distribution of graphite in ductile cast iron

The present work is a contribution to establish a simple new method for the characterization of spatial distribution of the graphite in ductile cast iron. This study is a trial to explain the correlation between the spatial distribution of the particles' sections in the 2D planner section and the spatial distribution of the same particles in the 3D space. The method is simple because it avoids the complex mathematical formulations and depends mostly on measurements. The model is based on distributing polydispersed spherical grains in a cubic unit according to three configurations, ordering, random and clustering. The reference sphere method is then applied for the 3-dimensional (3D) distribution and the reference circle method for the 2- dimensional (2D) distribution in the planner section, the local volume fraction, the 3D local particle density, the local area fraction and the 2D local particle density were investigated. The method was also applied on pearlitic and ferritic ductile cast iron specimens for verification of its usefulness.

The optimal Mercator projection and the optimal polycylindric projection of conformal type - case-study Indonesia

As a conformal mapping of the sphere S 2 R or of the ellipsoid of revolution E 2 A , B the Mercator projection maps the equator equidistantly while the transverse Mercator projection maps the transverse metaequator, the meridian of reference, with equidistance. Accordingly, the Mercator projection is very well suited to geographic regions which extend east-west along the equator; in contrast, the transverse Mercator projection is appropriate for those regions which have a south-north extension. Like the optimal transverse Mercator projection known as the Universal Transverse Mercator Projection (UTM), which maps the meridian of reference Λ0 with an optimal dilatation factor &ρcirc;=0.999 578 with respect to the World Geodetic Reference System WGS 84 and a strip [Λ0−Λ W ,Λ0 + Λ E ]×[Φ S ,Φ N ]= [−3.5∘,+3.5∘]×[−80∘,+84∘], we construct an optimal dilatation factor ρ for the optimal Mercator projection, summarized as the Universal Mercator Projection (UM), and an optimal dilatation factor ρ0 for the optimal polycylindric projection for various strip widths which maps parallel circles Φ0 equidistantly except for a dilatation factor ρ0, summarized as the Universal Polycylindric Projection (UPC). It turns out that the optimal dilatation factors are independent of the longitudinal extension of the strip and depend only on the latitude Φ0 of the parallel circle of reference and the southern and northern extension, namely the latitudes Φ S and Φ N , of the strip. For instance, for a strip [Φ S ,Φ N ]= [−1.5∘,+1.5∘] along the equator Φ0=0, the optimal Mercator projection with respect to WGS 84 is characterized by an optimal dilatation factor &ρcirc;=0.999 887 (strip width 3∘). For other strip widths and different choices of the parallel circle of reference Φ0, precise optimal dilatation factors are given. Finally the UPC for the geographic region of Indonesia is presented as an example.

Fitting Circles and Spheres to Coordinate Measuring Machine Data

This work addresses the problem of enclosing given data points between two concentric circles (spheres) of minimum distance whose associated annulus measures the out-of-roundness (OOR) tolerance. The problem arises in analyzing coordinate measuring machine (CMM) data taken against circular (spherical) features of manufactured parts. It also can be interpreted as the “geometric” Chebychev problem of fitting a circle (sphere) to data so as to minimize the maximum distance deviation. A related formulation, the “algebraic” Chebychev formula, determines the equation of a circle (sphere) to minimize the maximum violation of the equation by the data points. In this paper, we describe a linear-programming approach for the algebraic Chebychev formula that determines reference circles (spheres) and related annuluses whose widths are very close to the widths of the true geometric Chebychev annuluses. We also compare the algebraic Chebychev formula against the popular algebraic least-squares solutions for various data sets. In most of these examples, the algebraic and geometric Chebychev solutions coincide, which appears to be the case for most real applications. Such solutions yield concentric circles whose separation is less than that of the corresponding least-squares solution. It is suggested that the linear-programming approach be considered as an alternate solution method for determining OOR annuluses for CMM data sets.

Angles—Let’s treat them squarely

We suggest a self-consistent treatment of the dimensions and units of the geometric quantity “angle.” The method regards “angle” as a fundamental dimensional physical quantity, on a par with length, mass, time, etc. All units (whether angular or otherwise) are treated on an equal footing and balance out correctly; in particular, “radian” units need never be spuriously inserted or deleted. The method could find application in algebraic and calculus symbolic manipulation computer programs to correctly process units of physical quantities. The technique necessitates a minor modification of the relation “s=Rθ” and its consequences, rather than any modification of the units of other physical quantities (such as moment arms) as previously suggested by others. We make several important clarifying distinctions: (a) ω [SI: rad⋅s−1] for rotational motion (as in θ=ωt) versus Ω [SI: s−1] for simple harmonic motion [as in x=xm cos(Ωt)], (b) geometric trigonometric functions whose arguments are angles [SI: rad] versus mathematical trigonometric functions whose arguments are pure numbers, (c) simple harmonic motion versus uniform circular motion in the reference circle analogy.

Different mechanisms may underlie the performance in relative localization tasks.

Two different groups of subjects had to adjust two-dimensional stimuli, differing in size, shape and type (dot patterns or irregular contour figures), within a reference circle. The two groups performed under two different instructions. The first instruction stressed matching the centres of the stimulus and the circle, while the second required simply positioning the test stimulus in the middle of the reference circle. In two control experiments the subjects had to determine the position of the centres of each stimulus and of the reference circle. Under the first instruction the accuracy of performance, estimated by the variance of the responses, depended on the stimulus size, shape and type in agreement with previous results and models of relative localization. Under the second instruction, however, accuracy remained invariant. Possible mechanisms of relative localization that might differ at their first stages of localization of the separate stimuli are considered.

Analysis of Hipparcos Measurements: Positions, Proper Motions, Parallaxes

Using the first 12 months of HIPPARCOS mission data already reduced, a synthesis solution was obtained by both CERGA and ARI teams. The reduction includes two steps. In the first one the origins of individual reference circles are determined, thus constituting the HIPPARCOS celestial reference frame. This solution uses a subset of some 30 000 bright and evidently single stars in order to minimize possible corruptive effects on the system. In the second step, the abscissa measurements of all observed stars are substituted in the system and then processed star by star in a least squares adjustment providing the astrometric parameters (positions and parallaxes).The results of sphere solution and astrometric parameter determination are discussed. In this context error ellipses and internal errors are calculated. External errors are derived by comparison with suitable astrometric catalogues. Especially, for estimating the external errors of the HIPPARCOS measured FK5 stars the instrumental system was tied to the FK5 system by rigid rotations followed by comparisons of the positions with those of FK5. The mean internal errors of the HIPPARCOS positions of FK5 stars is 1.5 milliarcseconds (mas) while the standard deviation of the differences HIPPARCOS minus FK5 reaches 90 mas. For the 5022 measured parallaxes the mean internal and external errors are 3.8 mas and 16.7 mas, respectively. — The results of precision and comparisons with external data show that the accuracy predicted for the final catalogue can be reached.

Attentional modulation of size contrast.

A test circle surrounded by smaller context circles appears larger if presented in isolation, whereas a test circle surrounded by large context circles is seen as smaller than in isolation. Two experiments are reported indicating that this phenomenon, the Ebbinghaus illusion, depends on whether subjects are attending to the context circles. Subjects first saw a reference circle and then a briefly presented (150 msec) test circle. Their task was to determine whether the test circle was larger or smaller than the reference. The test circle was surrounded by smaller context circles of one colour arrayed along a horizontal axis centred on the test, and larger context circles of a different colour arrayed along a vertical axis centred on the test. Subjects judged both the size of the test and the colours of either the small or large context circles. Perceived test size changed systematically, depending on which context circles were task-relevant.

A boundary perturbation analysis for elastic inclusions and interfaces

A first-order boundary perturbation method based on Muskhelishvilli's complex variable representations is formulated for the two-dimensional elasticity problem of a nearly-circular inclusion embedded in an infinite dissimilar material. Universal relations which are independent of loading conditions are established among the solutions for a homogeneous infinite plane, a perfectly-circular inclusion and a slightly-perturbed non-circular inclusion. It is shown that the solution to a circular inclusion can be constructed algebraically from that of an infinite homogeneous plane while the stress distribution along the interface circle leads to the perturbation solutions for a nearly-circular inclusion. Explicit results arc given for inclusions with smooth polygon shapes by considering cosine wavy perturbations along a reference circle. A similar analysts is carried out for a bimaterial interface whose shape deviates slightly from a straight line. Our perturbation results can be used to study elastically-induced morphological perturbations of surfaces, interfaces, voids, precipitates and inclusions in a stressed solid. As an example, we demonstrate that, under sufficiently large stresses, material surfaces become unstable against a range of diffusional perturbations bounded by two critical wavelengths. Also, as suggested from our perturbation analysis and verified by a finite element calculation, even slight surface undulation caused by an unstable morphological perturbation can result in substantial stress concentration along the surface, which may cause plastic deformation or brittle fracture before the bulk stress reaches a critical level.

DISPA method in the analysis of Mössbauer spectra of metallic glasses

A plot of the DISPersion mode of a pure, ideal Lorentzian line versus the Absorption one (DISPA plot) gives a perfect circle. Non-Lorentzian profiles distort this reference circle in an unambiguous way. A modification of the DISPA method for the lineshape analysis of Mossbauer spectra of amorphous Fe83B17 and Fe40Ni40B20 pointed out convolutions of Gaussian and Lorentzian lines to be somewhat superior. Based on the previous results a construction of a hyperfine field distribution is proposed.

Minimisation of error on the effective profile of pinion type gear shaping cutters

Gear shaping cutters are provided with top-relief and rake angles to facilitate effective cutting. Due to this, the profile representing the cutting edge (effective profile) is altered. This paper outlines a method of obtaining the effective profile and its deviations from the theoretical involute form required. This paper also deals with a method that modifies the pressure angle, while maintaining zero deviation at the reference circle, so that the effective profile closer to the theoretical form is obtained after grinding the rake face. The Golden section optimization method is used to get the optimum value of the modified pressure angle. The effect of regrinding on the profile error of the cutting edge is also brought out. The method suggested in this paper will be useful to the designers and manufacturers of gear shaping cutters.

Astronomical Aspects of “Pranotomongso” of The 19th Century Central Java

It has been shown by Aveny (1981) that the development of indigenous astronomical systems in tropical cultures, whether the motive was religious or practical, centered toward a reference system consisting of zenith and nadir as poles and the horizon as a fundamental reference circle. Such a reference system differs remarkably to the celestial pole-equator (or ecliptic) systems employed by civilizations in temperate zones (also see Brennand, 1896; Stencel, et.al., 1976).In order to obtain more insight of the view expounded by Aveny (1981) the authors undertook a test case study of the astronomically related time-keeping practice in Java. “Pranotomongso” has been chosen as it is well documented since 1855. According to Daldjoeni (1984) the “pranotomongso” (literaly means the arrangements of seasons) functions well as a practical guide for agricultural activities for the rural peasants in Central Java.

Dispersion versus absorption (DISPA) plots as an index of static magnetic field inhomogeneity. Use for adjustment of spinning shims in a superconducting magnet

A new method for evaluating static magnetic field inhomogeneity in an NMR sample is described. Deviation from circularity of a plot of dispersion vs absorption (DISPA) provides a measure of the deviation of an experimental NMR lineshape from the ideal Lorentz shape. From DISPA plots constructed from spectra simulated from specified z-gradient (“spinning shim”) inhomogeneity terms, it is clear that the magnitude and direction of displacement of an experimental DISPA curve from its reference circle can serve to discriminate and quantitate the inhomogeneity in each of z, z 2, z 3, z 4, and z 5. As an index for monitoring field inhomogeneity, DISPA is more sensitive than monitoring the absolute area under a free induction decay (particularly for higher order spinning shims), and much faster and more discriminating (between different z n terms) than iterative fitting of the frequency-domain absorption spectrum. Although each of the experimental spinning shim coils does not produce a z gradient corresponding exactly to its labeled z n function, we find that experimental DISPA plots nevertheless correlate well with their theoretical counterparts for z 1 and z 2. DISPA has already proved useful for automated phasing of FT NMR spectra; the present work suggests that DISPA may offer a simple, rapid, sensitive method for testing shim coil designs and ultimately for manual or automated shimming of the static magnetic field as well.

Le nous à droite d'après un corpus d'éditoriaux de presse, 1973-1982

NOUS ON THE RIGHT Nous (we/us), which has a high frequency of occurrence in the corpus of right-wing press editorials (7 samples from 1973 to 1982), is often found, in terms of its presence and absence, in relation to on. Their copresence is contradictory : in general, when on precedes nous in the same chain of significance, it suggests that they are enemies (the « other » is the first to attack) ; when nous precedes on (there are very few examples) there is an homologous relationship between the two (on is a minor dimension of nous). Most frequently on, used either as a substitute or without definition, characterizes the others, the adversary. Nous is part of a more complex reference system. The analysis of the editorials leads to distinguish a nous as signatory (singular and in the same time collective and performative), a nous as French people, and a universal nous. Our grid is therefore very fluid. On their periphery there are others nous that are more difficult to pinpoint. The pronoun shifts, changes direction, is superimposed on itself while changing his circle of reference, as if to encompass the reader in an endless play of differences.

Automatic phase correction of fourier transform NMR spectra based on the dispersion versus absorption (DISPA) lineshape analysis

A method for automatic phase correction of Fourier transform NMR spectra bused on the dispersion versus absorption (DISPA) lineshape analysis is described. The DISPA display of a single misphased Lorentzian line gives a unit circle which has been rotated about the origin (relative to its “reference circle”) by a number of degrees equal to the phase misadjustment. This rotation, Φ, is a combination of the zero- and first-order phase angles at the frequency of the resonance. Calculation of Φ for two or more resonances allows the spectral phasing parameters to be determined and applied to correct the spectrum. This approach has been implemented in both automatic and “semi-automatic” modes.

A linkage for representing sine, cosine, and the reference circle

A linkage for representing sine, cosine, and the reference circle

10 to 60 Arcmin Fluctuations in the Cosmic Microwave Background

Considerable astronomical interest attaches to sensitive measurements of temperature fluctuations of the microwave background on scales of a few arcmins to a few degrees. We describe here the first in a series of experiments being carried out at Jodrell Bank which are aimed at providing reliable and repeatable information on these angular scales. The first experiment used the MK II 25m dish at λ6 cm and covered scales from 10 arcmin (the beamwidth) to 60 arcmin (twice the beamthrow). At this relatively long wavelength, the atmosphere has negligible effect on the observations and day to day repeatability consistent with receiver noise alone was obtained. The observations were made in wagging mode near the North Celestial Pole (NCP) so that the two beams alternately traced out a reference circle on the sky, radius 30 arcmin, over the course of 24 hours. The NCP field was chosen since a high sensitivity discrete source survey (Pauliny-Toth et al. 1978) was already available covering the area. This meant that antenna temperatures around the reference circle could be corrected for any source induced effects ≳0.4 mK. In addition control observations were made at positions 30 arcmin East and West of the central field, so that systematic effects due to interaction of telescope sidelobes with objects in the immediate telescope environment, could be monitored and removed.

Procedure for processing spectroscopic dispersion vs absorption (DISPA) line shapes

Abstract For a single Lorentzian line, a plot of dispersion versus absorption (DISPA) gives a perfect circle. For any line shape, the magnitude and direction of displacement of an experimental DISPA plot from its reference circle can be used to diagnose the line-broadening mechanism (e.g. multiple peak positions, multiple peak widths, chemical exchange, saturation broadening, etc.), based on the digitized envelope of a single spectrum. The present algorithm generates normalized absorption and dispersion data sets curves from digitized experimental spectra, and displays normalized reference and experimental DISPA curves in both video and hard copy analog recorder form. In order to symmetrize the final display and reduce compu tation time, the procedure first narrows the frequency range to 20 dispersion peak-to-peak widths on either side of the absorption maximum. The absorption and dispersion baselines are then (separately) flattened. The true absorption peak height and position are accurately estimated usinga polynomial approximation near resonance. The algorithm then normalized the baseline-flattened absorption and dispersion data sets, and plots the corresponding DISPA curve superimposed on a reference circle whose diameter is the calculated absorption peak height. Spacing of the displayed DISPA data points automatically increases with the frequency separation from the center of resonance, for faster plotting and reduced redundancy in display. As a Pascal program, the procedure executes directly on a Bruker Aspect 2000 computer, and can readily be adapted to other computers with Pascal compilers.

A chemotactic relationship between skeletal muscle nuclei and capillaries

The vascular beds of femoral biceps, soleus, and medial gastrocnemius of the rat were perfused with India ink to outline the capillary network. Histologic cross sections were stained with picric acid and basic fuchsin. By this method, the muscle fiber nuclei appeared red and could be clearly distinguished from the darker-stained capillary profiles. A specific anatomic relationship between capillaries and muscle fiber nuclei was tested against a random orientation by an analysis of independence. Systematic sampling was performed by positioning the center of an eyepiece reference circle on the uppermost point of each fiber profile. The frequencies of the four combinations (fiber nuclei and/or capillaries or neither) found within each test circle were recorded and stored in 2 × 2 contingency tables. The Z test of independence revealed a highly significant relationship between capillaries and fiber nuclei in all muscles examined. The nonrandom nucleus-related location of capillaries around muscle fibers was even more evident after pooling the individual muscle data in a single table ( P ⪡ 0.00001). These findings suggested a chemotactic attraction of capillaries by the muscle fiber nuclei. This observation is supported by the high concentration of cytoplasmic organelles present in nuclear regions of skeletal muscle fibers, that is well documented in the literature. These organelles may be responsible for the production and local secretion of chemotactic factors “to attract” capillaries, and hence provide for their characteristic orientation and distribution in muscle.

Dispersion versus absorption (DISPA) lineshape analysis. Effects of saturation, adjacent peaks, and simultaneous distribution in peak width and position

A plot of dispersion versus absorption (DISPA) for a single Lorentzian line gives a perfect circle. For other lineshapes, earlier papers in this series have shown that the direction and magnitude of the displacement of DISPA data from a reference circle (diameter equal to maximum absorption peak height) is characteristic of the line-broadening mechanism. In this paper, power saturation is shown to displace DISPA data symmetrically outside the reference circle. Adjacent peaks produce DISPA displacement that is detectable even for large peak separation (25 linewidths for a symmetrical doublet; 7 to 8 linewidths for the central line of a symmetrical triplet). Finally, a distribution in peak position is dominant over a distribution in linewidth in determining DISPA displacement. The DISPA plot shapes for these and 12 other line-broadening mechanisms are summarized in convenient reference form.