• Korean Journal of Applied Biomechanics
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• v.23 no.1
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• pp.53-62
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• 2013

The methods of fitting a circle to measured data, geometric fit and algebraic fit, have been studied profoundly in various areas of science. However, they have not been applied exactly to a biomechanics discipline for locating the center of rotation of a human joint. The purpose of this study was to generalize the methods to fitting spheres to the points in 3-dimension, and to estimate the center of rotation of a hip joint by three of geometric fit methods(Levenberg-Marquardt, Landau, and Sp$\ddot{a}$th) and four of algebraic fit methods(Delogne-K${\aa}$sa, Pratt, Taubin, and Hyper). 1000 times of simulation experiments for flexion/extension and ad/abduction at an artificial hip joint with four levels of range of motion(10, 15, 30, and $60^{\circ}$) and three levels of angular velocity(30, 60, and $90^{\circ}$/s) were executed to analyze the responses of the estimated center of rotation. The results showed that the Sp$\ddot{a}$th estimate was very sensitive to the marker near the center of rotation. The bias of Delogne-K${\aa}$sa estimate existed in an even larger range of motion. The Levenberg-Marquardt algorithm of geometric fit and the Pratt of algebraic fit showed the best results. The combination of two methods, using the Pratt's estimate as initial values of the Levenberg-Marquardt algorithm, could be a candidate of more valid estimator.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.8
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• pp.16-22
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• 1999

In this paper, an efficient algorithm for estimating real edge locations to subpixel values is described. Digital images are acquired by projection into image plane and sampling process. However, most of real edge locations are lost in this process, which causes low measurement accuracy. For accurate measurement, we propose an algorithm which estimates the real boundary between two adjacent pixels in digital imagery, with subpixel accuracy. We first define 1D edge operator based on the moment invariant. To extend it to 2D data, the edge orientation of each pixel is estimated by the LSE(Least Squares Error)line/circle fitting of a set of pixels around edge boundary. Then, using the pixels along the line perpendicular to the estimated edge orientation the real boundary is calculated with subpixel accuracy. Experimental results using real images show that the proposed method is robust in local noise, while maintaining low measurement error.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.33 no.8
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• pp.559-564
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• 2009

The variation in the shape of water droplet moving on atomistically smooth solid surface in the presence of a constant body force is simulated using molecular dynamics simulation. We investigated how the advancing and receding contact angle of the moving water droplet changes on a solid surface having various characteristic energies. From the MD simulation results, we obtained the density profile defined as the number of water molecules at a given position. Then, assuming the water droplet periphery to be a circle, we calculated the contact angles by using a nonlinear fitting of the half-density contour line. The present simulation clearly shows the different profile of the advancing and receding contact angle for these three different interaction potential between the water droplet and the solid surface.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.46 no.1
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• pp.56-62
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• 2009

In this paper we investigate an analytical approach for noise properties and geometric structure in Computed Radiography(CR) images of industrial steel-tubes. Over thirty diverse radiographic images are sampled from industrial radiography measurements according to radiation intensity. Each image consists of three regions; background, thickness and inner-tube. Among these the region of inner-tube is selected for the object of analysis. Geometric structure which includes the noise generation is analyzed by the statistical and functional methodology. The analysis is carried on spacially and line by line. It verifies the geometrical transfigure from the circle configuration of steel-tube and noise variation. The estimation of fitting function and its error are the geometric factors. The statistics such as standard deviation, mean and signal-to-noise ratio are noise parameters for discrimination. These factors are considered under the intensity variation which is the penetrative strength of radiation. The analysing results show that the original geometry of circle is preserved in the form of elliptic or short/long diameter circle, and the noise deviation has increased inverse proportional to the radiation intensity.

• Industrial Engineering and Management Systems
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• v.6 no.2
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• pp.94-105
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• 2007

Measurement technology plays an important role in discrete manufacturing industry. Probe-type coordinate measuring machines (CMMs) are normally used to capture the geometry of part features. The measured points are then fit to verify a specified geometry by using the least squares method (LSQ). However, it occasionally overestimates the tolerance zone, which leads to the rejection of some good parts. To overcome this drawback, minimum zone approaches defined by the ANSI Y14.5M-1994 standard have been extensively pursued for zone fitting in coordinate form literature for such basic features as plane, circle, cylinder and sphere. Meanwhile, complex features such as torus have been left to be dealt-with by the use of profile tolerance definition. This may be impractical when accuracy of the whole profile is desired. Hence, the true deviation model of torus is developed and then formulated as a minimax problem. Next, a relatively new and simple population based evolutionary approach, particle swarm optimization (PSO), is applied by imitating the social behavior of animals to find the minimum tolerance zone torusity. Simulated data with specified torusity zones are used to validate the deviation model. The torusity results are in close agreement with the actual torusity zones and also confirm the effectiveness of the proposed PSO when compared to those of the LSQ.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.6
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• pp.96-104
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• 2003

This paper presents the measurement and correction method of PCB alignment errors for PCB screen printer. Electronic equipment is getting smaller and yet must satisfy high performance standard. Therefore, there is a great demand for PCB with high density. However conventional PCB screen printer doesn't have enough accuracy to accommodate the demand for high-resolution circuit pattern and high-density mounting capacity of electronic chips. It is because the alignment errors of PCB occur when it is loaded to the screen printer. Therefore, this study focuses on the development of the system which is able to measure and correct alignment errors with high-accuracy. An automatic optical inspection part measures the PCB alignment errors using machine vision, and the high-accuracy 3-axis stage makes correction for these errors. This system used two CCD cameras to get images of two fiducial marks of PCB. The centers of fiducial marks are obtained by using moment, gradient method. The first method is calculating the centroid by using first moment of blob, and the latter method is calculating the center of the circle whose equation is obtained by curve-fitting the boundaries of fiducial mark. The operating system used to implement the whole set-up is carried in Window 98 (or NT) environment. Finally we implemented this system to PCB screen printer.

• Korean Journal of Computational Design and Engineering
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• v.10 no.2
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• pp.114-120
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• 2005

This paper presents a novel method for radius measurement of fillet regions of polygonal models by using optimum onhogonal planes. The objective function for finding an optimum onhogonal plane is designed based on the orthogonality between the normal vectors of the faces in a filet region and the plane that is to be found. Direct search methods are employed to solve the defined optimization problem since no explicit derivatives of the object function can be calculated. Once an optimum orthogonal plane is obtained, the intersection between the onhogonal plane and the faces of interest is calculated, and necessary point data in the fillet region for measuring radii are extracted by some manipulation. Then, the radius of the fillet region in question is measured by least squares fitting of a circle to the extracted point data. The proposed radius measuring method could eliminate the burden of defining a plane for radius measurement, and automatically find a necessary optimum orthogonal plane. It has an advantage in that it can measure fillet radii without prior complicated segmentation of fillet regions and explicit information of neighboring surfaces. The proposed method is demonstrated trough some mea-surement examples.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 1997.04a
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• pp.77-87
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• 1997

The earthquake data(M$\geq$4.0) for post-1900 in the Korean Peninsula show temporal variation with active and quiet periods. The pattern is quite similar to northeastern China and Inner Zone of Southwest Japan. Yeongweol earthquake occurred in the seismic gap region of the Korean Peninsula. This is the first medium-size earthquake in inland region of the southern peninsula since 1978. The intensity based on the felt area estimation of about 400 places shows MMI III-Ⅷ in inland region. IIon Cheju Island and Ion Ulreung Island. The isoseismal of MMI Ⅶ shows an elongated circle in the direction of NE-SW and covers some parts of Jungdong-myon, Yeongweol-kun, Sindong-eup and Nam-myun, Jeongseon-kun. There occurred quite strong shaking, numerous cracks on the walls of buildings, falling and movement of slate and tiles on the roofs, falling of tiles from the wall and falling of materials from desks, rook falling from mountain and collapse of gravel lauers on the river side. The least square fitting of the intensity data of the Yeongweol earthquake by a popular intensity attenuation relation yields the following : I=Io＋1.82249 - 0.65295*InR - 0.00707*R

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.2
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• pp.296-303
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• 1987

The composite gear which is composed of involute curve and circular arc has been studied. In the vicinity of pitch point, its profile is an involute curve, and in the dedenum, a circular arc. The curve in the dedendum is generated by the circular arc of the mating gear. Though the available range between minimum and maximum radius of circular arc can be given by existing tooth profile equation, there was no formulation which relates design parameters to the desired radius. It is attempted to get the formula for the radius of circular arc as a function of design parameters, such as unwounded angle, number of teeth, module, and pressure angle. The radius of circular arc, the chordal tooth thickness at working root circle, nominal bending stress, Hertz stress and contact ratio obtained from derived formula are compared with those of the existing design criteria. And these are compared with those of involute gear.

• Geophysics and Geophysical Exploration
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• v.19 no.1
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• pp.1-10
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• 2016

The hypocenter distribution of microseismic events generated by hydraulic fracturing for shale gas development provides essential information for understanding characteristics of fracture network. In this study, we evaluate how inaccurate velocity models influence the inversion results of two widely used location programs, hypoellipse and hypoDD, which are developed based on an iterative linear inversion. We assume that 98 stations are densely located inside the circle with a radius of 4 km and 5 artificial hypocenter sets (S0 ~ S4) are located from the center of the network to the south with 1 km interval. Each hypocenter set contains 25 events placed on the plane. To quantify accuracies of the inversion results, we defined 6 parameters: difference between average hypocenters of assumed and inverted locations, $d_1$; ratio of assumed and inverted areas estimated by hypocenters, r; difference between dip of the reference plane and the best fitting plane for determined hypocenters, ${\theta}$; difference between strike of the reference plane and the best fitting plane for determined hypocenters, ${\phi}$; root-mean-square distance between hypocenters and the best fitting plane, $d_2$; root-mean-square error in horizontal direction on the best fitting plane, $d_3$. Synthetic travel times are calculated for the reference model having 1D layered structure and the inaccurate velocity model for the inversion is constructed by using normal distribution with standard deviations of 0.1, 0.2, and 0.3 km/s, respectively, with respect to the reference model. The parameters $d_1$, r, ${\theta}$, and $d_2$ show positive correlation with the level of velocity perturbations, but the others are not sensitive to the perturbations except S4, which is located at the outer boundary of the network. In cases of S0, S1, S2, and S3, hypoellipse and hypoDD provide similar results for $d_1$. However, for other parameters, hypoDD shows much better results and errors of locations can be reduced by about several meters regardless of the level of perturbations. In light of the purpose to understand the characteristics of hydraulic fracturing, $1{\sigma}$ error of velocity structure should be under 0.2 km/s in hypoellipse and 0.3 km/s in hypoDD.