• Journal of the Korean Society for Precision Engineering
• /
• v.17 no.7
• /
• pp.156-161
• /
• 2000

Least Squares and Minimum Zone method are known for obtaining a datum or a continuous approximate function of measured data. This study is for a Minimum Zone algorithm for a circle, which is useful to obtain the exact roundness from the reference circle of measured data. The proposed method is compared with the Least Squares Limacon method and Chrystal-Peirce algorithm. A computational algorithm for the Minimum Zone circle is suggested and results in less roundness than the other two methods. This Minimum Zone circle method will be used for other geometrical measured data, such as plane or sphere for obtaining the exact flatness or sphericity.

• Journal of applied mathematics & informatics
• /
• v.7 no.3
• /
• pp.983-994
• /
• 2000

We consider the problem of determining the circle of best fit to a set of data points in the plane. In [1] and [2] several algorithms already have been given for fitting a circle in least squares sense of minimizing the geometric distances to the given data points. In this paper we present another new descent algorithm which computes a parametric represented circle in order to minimize the sum of the squares of the distances to the given points. For any choice of starting values our algorithm has the advantage of ensuring convergence to a local minimum. Numerical examples are given.

• Journal of the Korean Statistical Society
• /
• v.31 no.2
• /
• pp.251-259
• /
• 2002

Lagged regressor models with general stationary errors independent of the regressors are considered. The regressor process is unstable having characteristic roots on the unit circle. If the order of the lag matches the number of roots on the unit circle, the ordinary least squares estimator (OLSE) is asymptotically efficient in that it has the same limiting distribution as the generalized least squares estimator (GLSE) under the same normalization. This result extends the well-known result of Grenander and Rosenblatt (1957) for asymptotic efficiency of the OLSE in deterministic polynomial and/or trigonometric regressor models to a class of models with stochastic regressors.

• Transactions of the Korean Society of Machine Tool Engineers
• /
• v.12 no.4
• /
• pp.17-22
• /
• 2003

This paper presents a new circular curve fitting approach of articulated manipulators, based on least square. The approach aims at gaining the interpolation of circle from n data points, under the condition that the fitted circle should pass both a starting point and an ending point. First a spherical fitting should be performed, using least squares. Then the circular curve fitting can be resulted from the intersection of the fitted sphere and the plane obtained from 3 points, i. e., a starting point, an ending point and the center of a sphere. The proposed algorithms are shown to be efficient by using MATLAB-based simulation.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2002.10a
• /
• pp.570-575
• /
• 2002

This paper presents a new circular curve fitting approach of articulated manipulators, based on pseudoinverses. The paper aims at gaining the interpolation of circle from n data points, under the condition that the fitted circle should pass both a start point and an end point. In this paper, two algorithms of circular interpolation are presented. Prior to circular interpolation, are a spherical fitting should be performed, using least squares. In the first algorithm, the relationship between point data and normal vector on the sphere is used. In the second algorithm. the equation of plane which can be obtained from 3 points, i.e., a start point, an end point, and center of a sphere. The proposed algorithms are show to be efficient by using MATLAB-based simulation.

• Journal of the Semiconductor & Display Technology
• /
• v.9 no.1
• /
• pp.11-16
• /
• 2010

Wafer Pre-Alignment is to find the center and the orientation of a wafer and to move the wafer to the desired position and orientation. In this paper, an area camera based pre-aligning method is presented that captures 8 wafer images regularly during 360 degrees rotation. From the images, wafer edge positions are extracted and used to estimate the wafer's center and orientation using least squares circle fitting. These data are utilized for the proper alignment of the wafer. For accurate alignments, camera calibration methods using high order polynomials are used for converting pixel coordinates into real-world coordinates. A complete pre-alignment system was constructed using mechanical and optical components and tested. Experimental results show that alignment of wafer center and orientation can be done with the standard deviation of 0.002 mm and 0.028 degree, respectively.

• Journal of the Korean Society of Manufacturing Technology Engineers
• /
• v.8 no.4
• /
• pp.52-60
• /
• 1999

In this study the effect of roundness error with respect to the cutting conditions using the external cylindrical work piece by end mill cutting in a machining center was studied. the end mill used in this study is HSS coated with Ti-N which is of Ø 12-4 flutes. The material of workpiece is SM20C and cutting oil is used as a cooling flued The cutting experiments were carried out for the several cutting conditions(depth of cut height of end mill feed rate revolution per minute and cutting direction) and their roundness effects were compared using the least squares circle measuring method. The experimental results are summarized as follows : 1) The cutting depth is dominant for the roundness of a cylindrical work piece and the cutting speed must be determined precisely when the cutting depth is large 2) When the cutting direction in circular manufacturing is the same with the spindle rotation i.e up-cutting condition the surface roundness is also improved.

• Archives of Pharmacal Research
• /
• v.5 no.2
• /
• pp.79-86
• /
• 1982

Sulfisoxazole, $C-{11}H_{13}N_{3}S$, crystallized in the orthohombic system, space group Pbca, with a = 14.492(1), b = 11.563(1), c = 14.900(2) $\AA$ and Z = 8. Intensities for 1867(1360 observed) unique reflections were measured on a four-circle diffractometer wirh CuKa radiation ($\lambda$ = 1.5418$\AA$). The structure was solved by heavy atom methods and refined by full-matrix least-squares procedures to a final R of 0.094. The benzene ring plane makes an angle of $68^{\circ}C$ with the plane of the isoxazole ring, which is plannar. The conformational angle formed by the torsional angle C(4)-S-N(2)-C(7) is $54^{\circ}C$. There are two intermolecular hydrogen bonds in the structure. One of them is of the type N-H...H with the length 2.915$\AA$. Thus two dimensional networks of hydrogen bonds form infinite moelcular sheets parallel to the (001) plane. Adjacent sheets are bound together by van der Waals forces.

• Journal of the Korean Society for Precision Engineering
• /
• v.27 no.4
• /
• pp.33-39
• /
• 2010

Manufacturing accuracy of a precision instrument was essential to stability and efficiency of the product. Accordingly, geometrically accuracy management of precision instrument was very becoming the technique in order to design and manufacturing for machine. In this study, Measuring System is developed for extra long roller using non-contact sensor. Futhermore, It's studied by Geometric Tolerance. Exact roundness is obtained to Least Squares method from the reference circle of measured data. Measuring System is analyzed point of measurement and straightness of extra long roller is evaluated by FEM.

• Bulletin of the Korean Chemical Society
• /
• v.3 no.1
• /
• pp.9-13
• /
• 1982

Sulfametrole, $C_9H_{10}N_4O_3S_2$, crystallizes in the monoclinic system, space group $P2_1/n$ , with a = 8.145(2), b = 16.505(4), c = 9.637(1)${\AA},{\beta}=103.72(1)^{\circ},D_m=1.52gcm^{-3}$,Z=4.Intensities for 3594(2143 observed) unique reflections were measured on a four-circle diffractometer with Mo $K{\alpha}$ radiation $({\lambda}=0.71069{\AA})$. The structure was solved by direct method and refined by full-matrix least squares to a final R of 0.070. The geometrical features of the thiadiazole ring indicate some ${pi}$-electron delocalization inside the ring. The least squares planes defined by the benzene and thiadiazole rings are nearly perpendicular to each other(dihedral angle; $93.9^{\circ}$ ). All the potential hydrogen-bond donor atoms in the molecule, N(1) and N(2), are included in the hydrogen bonding. The molecules through hydrogen bonding form three dimensional network.