Divided Circle Research Articles

When the West is far away: Romanian attempts to withdraw from World War II (1943-1944), Finnish views

This article approaches the Romanian foreign policy stakes in the aftermath of the Stalingrad Battle as seen from the perspective of a comrade-in-arms country, Finland, which shared with Romania many of the assumptions, fears and anxieties with regard to the outcome of the war. The article is shaped in Stephen M. Walt’s understanding of balancing and bandwagoning, Romania and Finland choosing Germany over the Soviet Union mainly for the reason that the latter was perceived as the biggest security threat and the former as the only possible deterrent and support. The material focuses on the analysis of Eduard Hjalmar Palin’s diplomatic dispatches from Bucharest. On one hand, they were the main source of information for the Finnish decision-makers with regard to the Romanian international situation and its foreign and domestic policies. On other hand, Palin was an experienced diplomat, with excellent connections in the Romanian society and enjoyed access to confidential information in the governmental circles due to a Romanian-Finnish agreement of summer of 1941. We can see, for instances, cases when Ion and Mihai Antonescu confided to the Finnish envoy Führer Adolf Hitler’s statements which could affect the situation in Finland or help its leaders to take decisions. The article shows how divided Romanian governmental and opposition circles were, not only between but also among themselves. By reading these diplomatic reports, we could also acknowledge the widening split between the views of the two most prominent Romanian governmental leaders, Ion and Mihai Antonescu, thus complementing other sources of information already published. We can also learn about some peace plans of Romanian opposition groups, some of whom are little known from other documentary sources.

High efficiency gears synthesis by avoid the interferences

The paper presents an original method to determine the efficiency of the gear, the forces of the gearing, the velocities and the powers. It is analyzing the influence of a few parameters concerning gear efficiency.These parameters are:z1 - the number of teeth for the primary wheel of gear; z2 - the number of teeth of the secondary wheel of gear; alpha0 - the normal pressure angle on the divided circle; beta - the inclination angle. With the relations presented in this paper, it can synthesize the gear’s mechanisms. Today, the gears are present everywhere, in the mechanical’s world (In vehicle’s industries, in electronics and electro-technique equipments, in energetically industries, etc). Optimizing this mechanism (the gears mechanism), we can improve the functionality of the transmissions with gears. At the gear mechanisms an important problem is the interference of the teeth. To avoid the interference between teeth, we must know the minimum number of teeth of the driving wheel, in function of the pressure angle (normal on the pitch circle, alpha0), in function of the tooth inclination angle (beta), and in function of the transmission ratio (i).

GEAR DESIGN

The paper presents an original method to determine the efficiency of the gear, the forces of the gearing, the velocities and the powers. The originality of this method relies on the eliminated friction modulus. The first chapters are analyzing the influence of a few parameters concerning gear efficiency. These parameters are: z1 - the number of teeth for the primary wheel of gear; z2 - the number of teeth of the secondary wheel of gear; alpha0 - the normal pressure angle on the divided circle; beta - the inclination angle. With the relations presented in this paper, it can synthesize the gear’s mechanisms. Today, the gears are present everywhere, in the mechanical’s world (In vehicle’s industries, in electronics and electro-technique equipments, in energetically industries, etc.). Optimizing this mechanism (the gears mechanism), we can improve the functionality of the transmissions with gears. At the gear mechanisms an important problem is the interference of the teeth. To avoid the interference between teeth, we must know the minimum number of teeth of the driving wheel, in function of the pressure angle (normal on the pitch circle, alpha0), in function of the tooth inclination angle (beta), and in function transmission ratio (i). The last chapter presents an original method to make the geometric synthesis of the gear, having in view the minimum number of teeth of the driving wheel. The classical methods use many different relations to determine the minimum number of teeth of the driving wheel. By this paper we want to give a unitary method to determine the minimum number of teeth of the driving wheel 1, to avoid the interference between the teeth of the two wheels (of the gear).

Calibration of angle artifacts and instruments using a high precision angle generator

Various angle artifacts and instruments are used in precision engineering, and their calibrations are important to ensure high accuracy and reliability in angle metrology. In this paper, we present uncertainty analysis and calibrations of several angle artifact and instruments to evaluate the performance of the high precision angle generator which is newly developed as the primary angle standard of Korea Research Institute of Standards and Science (KRISS). The configuration of the angle generator is explained shortly, which uses multiple ultrasonic motors and a self-calibratable encoder adopting the equal-division-averaged (EDA) method. The expanded uncertainty (k = 2) of the angle generator, which are mainly contributed by nonlinearity and scale error of a divided circle, was evaluated less than 0.03″. The calibration result of a high precision angle encoder was compatible with that of manufacturer within the expanded uncertainty of calibration, 0.04″. Using the calibration result of an electronic autocollimator, the nonlinearity error of the angle generator was analyzed and a calibration method is proposed to reduce the nonlinearity error related to the signal period of the divided circle. In the calibration of a 36-face optical polygon, we applied the complete closure method to obtain the error of the angle generator separately, and its magnitude was less than 0.015″, which is less than half of the estimated uncertainty of the angle generator.

Note: High precision angle generator using multiple ultrasonic motors and a self-calibratable encoder

We present an angle generator with high resolution and accuracy, which uses multiple ultrasonic motors and a self-calibratable encoder. A cylindrical air bearing guides a rotational motion, and the ultrasonic motors achieve high resolution over the full circle range with a simple configuration. The self-calibratable encoder can compensate the scale error of a divided circle (signal period: 20") effectively by applying the equal-division-averaged method. The angle generator configures a position feedback control loop using the readout of the encoder. By combining the ac and dc operation mode, the angle generator produced stepwise angular motion with 0.005" resolution. We also evaluated the performance of the angle generator using a precision angle encoder and an autocollimator. The expanded uncertainty (k = 2) in the angle generation was estimated less than 0.03", which included the calibrated scale error and the nonlinearity error.

Loci Conversion and Corner Smoothing with PH Curves in CNC System

Free-form surface interpolation functions give more advantages in machining than the traditional line and circle functions. A method is developed to convert lines and circles into Pythagorean-hodograph (PH) curves. In order to get smooth machining process the PH curve is used to replace the joints of the circular/linear elements by the connection situation. The slope of line is used to get the tangent vector in the line conversion. When converting a circle to a PH curve, points of the divided circle are introduced to compute the vectors. The methods of computing tangent vectors are proposed according to the slope of the line and the quadrant of the circle. The transformation errors from lines and circles to PH curves are computed. In the corner smoothing process the tangent vectors are computed by the connection between lines and circles. Replacement errors at the joints are computed for the use of PH curve. The results demonstrate the feasibility of the conversion from line and circle to PH curve. The PH curves at the joints of the circular and linear elements show continuous trajectory.

Self-calibration of divided circles on the basis of a prime factor algorithm

A new method for the self-calibration of divided circles is presented which is based on a known prime factor algorithm for the discrete Fourier transform (DFT). The method, called prime factor division (PFD) calibration, is of interest in angle metrology specially for self-calibrating angle encoders, and generally for a significant shortening of the cross-calibration between two divided circles. It requires that the circular division number N can be expressed as a product N = R × S, whereby the factors R and S are relatively prime integer numbers. For the self-calibration of a divided circle, N difference measurements between R angle positions in a regular distribution and one reference angle position determined by S are evaluated by a two-dimensional DFT, yielding the N absolute division errors. The factor R is preferably chosen small, down to a minimum of R = 2, whereas the factor S may be as large as appropriate for the division number N of interest. In the case of a cross-calibration between two divided circles, the PFD method reduces the number of measurements necessary from N2 to (R + 1) × N. Experimental results are demonstrated for the calibrations of an optical polygon with 24 faces (prime factor product 3 × 8) and a gearwheel with 44 teeth (prime factor product 4 × 11).

Gearrs Design for the Mechanismms Highest Efficiency

The paper presents an original method to determine the efficiency of the gear. The originality of this method relies on the eliminated friction modulus. The paper is analyzing the influence of a few parameters concerning gear efficiency. These parameters are z1 - the number of teeth for the primary wheel of gear; z2- the number of teeth of the secondary wheel of gear; α0 - the normal pressure angle on the divided circle; β - the inclination angle. With the relations presented in this paper, one can synthesize the gear’s mechanisms.

Uncertainty Analysis for Angle Calibrations Using Circle Closure.

We analyze two types of full-circle angle calibrations: a simple closure in which a single set of unknown angular segments is sequentially compared with an unknown reference angle, and a dual closure in which two divided circles are simultaneously calibrated by intercomparison. In each case, the constraint of circle closure provides auxiliary information that (1) enables a complete calibration process without reference to separately calibrated reference artifacts, and (2) serves to reduce measurement uncertainty. We derive closed-form expressions for the combined standard uncertainties of angle calibrations, following guidelines published by the International Organization for Standardization (ISO) and NIST. The analysis includes methods for the quantitative evaluation of the standard uncertainty of small angle measurement using electronic autocollimators, including the effects of calibration uncertainty and air turbulence.

An Autocollimation Circle Reading System for the Infrared Meridian Instrument

A new autocollimation circle reading system is proposed for the reflector meridian circle (Nemiro and Streletsky, 1988). The instrument will be used for observations in the K-infrared waveband. Instead of the divided circle fixed to the instrument tube the new system has small spherical mirrors polished at the lateral surfaces of the primary mirror. The primary mirror is made from sitall and has an autocollimation system aimed at monitoring its optical axis position. The small spherical mirrors of the circle reading system link the circle readings with the primary's optical axis. The divided circles are fixed unmovable opposite to both lateral surfaces of the primary's optical block. Both surfaces have four spherical mirrors. The distance between the divided circles and the mirrors is equal to the mirrors' radii of curvature. The scales of each circle are illuminated from outside (where the measuring microscopes are placed). The mirrors form autocollimated images of the divisions at the plane of the divisions itself. Averaged coordinates of a division and its autocollimated image give the position of the mirror's optical center, and the semi-difference of the coordinates gives the angular position of the telescope. So, the measurements of the circle positions are differential ones, and any displacements of the microscope zero-points are not critical. The precision of measurements is estimated to be better then 0.05″ (random) and 0.005″ (systematical). The work was supported by the Russian Foundation of Fundamental Investigations (the project's code is 93-02-17095).

The Modernization of the Pulkovo Photographic (Photoelectric) Vertical Circle by a CCD Array

The Zverev photographic vertical circle (PVC) of the Pulkovo observatory is in the process of modernization. The features of the vertical circle are: a)Maksutov mirror-lens optical system with small aberrations and wide passband: aperture: 20 cm, focal length: 200 cm, focal scale: 103 arcsec/mm.b)Very compact instrument: 140 cm total length, 60 cm — tube.c)Wide field: 25 × 25 mm = 40′ × 40′. Wide-field imaging can be combined with meridian observations.d)Easily-reversible instrument: reversing takes less than 30 seconds.e)Two divided vertical circles of glass. Photoelectric circle reading microscopes.f)Photographic micrometer in focal plane. This will be changed with a CCD micrometer.

Stability of the division corrections for a metal declination circle

The long term evolution of the metallic divided circle mounted on the Bordeaux meridian instrument is presented. Results of three independent determinations carried out in 1987 with different ambient temperatures show deviations the major part of which could be due to small malfunction of the photoelectric reading microscopes. The importance of a regular monitoring of the division errors is stressed.

Absolute Determinations of Star Declinations From Pole to Pole

The most widely spread method of determination of star declinations is Bessel's method. Alhough it gives good agreement between star declinations obtained from observations of stars in upper and lower culminations, it leads to great systematic errors if the system of the instrument has an error of the type such as flexure or errors of divided circle. Besides, in the determination of correction of latitude (Δφ) and refraction (Δμ) considerable correlation between them exists.

Determination of the Division Corrections of the Bordeaux Declination Circle by the Benevides-Boczko Method

The automatic declination reading system implemented on the Bordeaux meridian circle with a new divided circle is shortly presented. The determination of the division errors by the Benevides-Boczko method was carried out in December 1982 and in March 1983: the standard deviation between the two sets of corrections is about 0.015″.

Spinners and Chartmoves:

A practical child management procedure is presented which incorporates self-recording, variable schedules of reinforcement, and a practical data collection system. The proposed system has two basic components, chartmoves and spinners. The chart is generally a picture with 30 to 100 dots and functions as a data collection system and indicates when a reinforcer has been programmed. Reinforcers are set up by randomly placing large dots (reinforcer dot), which make up the picture. When a child exhibits an appropriate target behavior, he is allowed to connect two dots on the picture. Each dot is covered with a scratch off ink; if the last dot connected is large the child receives a reinforcer. Chartmoves (connection of dots) are dated and initialed by the teacher allowing a record of progress to be kept with little effort by the teacher or parent. The second component to the system is the spinner. The spinner is an unevenly divided circle (generally five sections) with each section containing a reinforcer, plu...

Polaroid ED-10 Instrument camera attachment for divided circle spectrometers

First Page

Calibration of Ellipsometer Divided Circles*

Calibration of Ellipsometer Divided Circles*

High-Precision Pointing Interferometer

By adjusting a Kösters prism interferometer so that the zero-order fringe is parallel to the beam splitter and to the apex, and is as far from the apex as possible, a parallel-beam Michelson-type interferometer was produced which is capable of pointing with a precision of 0.02 sec of arc. The sensitivity is proportional directly to the beam spacing and inversely to the wavelength. With beam separation of approximately 56 mm and green Hg light, each fringe passage represents 1 sec of arc mirror rotation. Angles of over 2000 sec can easily be measured. Described are schemes for using the instrument for measurement of film thickness, plane mirror rotation, divided circle accuracy by use of a stepping mirror, refractive index and difference, ball-bearing sphericity, absolute pressure, tilt, etc. Observation of fringes, which are located at the mirror surface, is conveniently accomplished by means of a standard alignment telescope, which may be attached to the interferometer or separated many meters from it. Use of mixed monochromatic and white light permits identification of the zero-order fringe in the presence of higher order fringes.

Position transducer using a divided circle and coded scale

A small transducer is described in which a coded scale is used to distinguish the lines on a divided circle. This unit is intended as a positional reference in a large data-collecting system. The circle and code are both detected photoelectrically, though using very different cells and lamps. In order to keep the instrument diameter small, the coded scale is made in drum form.

The Ottawa Mirror-Transit Telescope.

The design of the Ottawa Mirror Transit, which is located near the main building of the Dominion Observatory, is well advanced and some preliminary test observations have begun. It is housed in a well-insulated building which is cooled in order to hold the instrument at anticipated nighttime temperatures. The north and south ends move apart on rails, completely exposing the instrument and giving a clear line of sight to within 130 of each horizon along the meridian. An 11-inch diameter, 2-inch thick quartz mirror is held in the central axis with its plane in the axis of rotation. The mirror reflects the starlight into either one of two horizontal telescopes, which are each of 10 inches aperture and 168 focal length, there being a gap of some 160 inches between the two objective glasses with the axis assembly midway between. Each telescope can "see" 200 or more beyond the zenith, providing a convenient overlap. The direction of the mirror normal is obtained from four, or possibly six, of the conventional microscopes, having objectives of five inches focal length, magnification 6 x. These photograph the divided circle, which is marked in three-minute intervals. The behavior of the mirror in its various attitudes is determined by autocollimating telescopes which view small mirrors cemented to the east and west flanks of the main mirror. Two bright-wire recticles, one fixed, and one movable with the star image, are placed, face to face, at the prime foci of the telescopes; and all images are transported about six inches by unit magnification to the film plane. Observations may be by photographic or visual means, the lead screw in either case being driven at the correct velocity by an analogue computer.