• Korean Journal of Computational Design and Engineering
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• v.5 no.2
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• pp.168-174
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• 2000

A biarc is a curve connecting two circular arcs with the constraints of tangent continuity so that it can represent the free form currie approximately connecting several biarcs with the tangent continuity. Since a biarc consists of circular arcs, the offset curve of the curve represented by biarcs can be easily obtained. Besides. if the tool path is represented by biarcs, the efficiency of machining is improved and the amount of data is decreased. When approximating a curve with biarcs, the location of the point where two circular arcs meet each other plays an important part in determining the shape of a biarc. In this thesis, the optimum point where two circular arcs meet is calculated using the tangent information of the curve to approximate so that it takes less calculation time to approximate due to the decrease of the number of iterations.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.4
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• pp.709-714
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• 2017

The curved panel is widely used for display of TVs and smart phones. This paper proposes a new auto-focusing method for curved panel inspection system. Since the distance between the camera and the panel varies with the curve position, the camera should change its focus at every inspection time. In order to reduce the focusing time, we propose an effective focusing method that considers the mathematical model of panel curve. The Lagrange polynomial equation is applied to modeling the panel curve. The foci of initial three points are used to get the curve equation, and the other foci are calculated automatically from the curve equation. The experiment result shows that the proposed method can reduce the focusing time.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.809-823
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• 2020

In this article, we study the deformation theory of locally free sheaves and Hitchin pairs over a nodal curve. As a special case, the infinitesimal deformation of these objects gives the tangent space of the corresponding moduli spaces, which can be used to calculate the dimension of the corresponding moduli space. The deformation theory of locally free sheaves and Hitchin pairs over a nodal curve can be interpreted as the deformation theory of generalized parabolic bundles and generalized parabolic Hitchin pairs over the normalization of the nodal curve, respectively. This interpretation is given by the correspondence between locally free sheaves over a nodal curve and generalized parabolic bundles over its normalization.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1269-1281
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• 2020

In this article, we show that a pseudo-Hermitian magnetic curve in a normal almost contact metric 3-manifold equipped with the canonical affine connection ${\hat{\nabla}}^t$ is a slant helix with pseudo-Hermitian curvature ${\hat{\kappa}}={\mid}q{\mid}\;sin\;{\theta}$ and pseudo-Hermitian torsion ${\hat{\tau}}=q\;cos\;{\theta}$. Moreover, we prove that every pseudo-Hermitian magnetic curve in normal almost contact metric 3-manifolds except quasi-Sasakian 3-manifolds is a slant helix as a Riemannian geometric sense. On the other hand we will show that a pseudo-Hermitian magnetic curve γ in a quasi-Sasakian 3-manifold M is a slant curve with curvature κ = |(t - α) cos θ + q| sin θ and torsion τ = α + {(t - α) cos θ + q} cos θ. These curves are not helices, in general. Note that if the ambient space M is an α-Sasakian 3-manifold, then γ is a slant helix.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.429-430
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• 2006

To estimate the fatigue life of flange-shaft assembly, fatigue test for flange material and bending fatigue test for flange-shaft assembly were conducted. Also, finite element analysis for flange-shaft assembly was conducted. Then, we have changed the obtained P-N curve to S-N curve using the finite element analysis results which were stress values at the location of fracture. The S-N curve of flange material itself was almost consistent with that of flange-shaft assembly, so it seems that the fatigue life of flange-shaft assembly could be estimated by using S-N curve for flange material and the stress at the location of fracture calculated by finite element methods.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.24 no.6
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• pp.696-702
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• 2015

This paper suggests a new method for making a navigation path by using Bezier curve in order to improve the navigation performance used to avoid obstacles during a robot soccer game. We analyzed the advantages and disadvantages of both vector-field and limit-cycle navigation methods, which are the mostly widely used navigation methods for avoiding obstacles. To improve the disadvantages of these methods, we propose a new design technique for generating a more proper path using Bezier curve and describe its advantages. Using computer simulations and experiments, we compare the performance of vector-field navigation with that of Bezier curve navigation. The results prove that the navigation performance using Bezier curve is relatively superior to the other method.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.4 s.97
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• pp.129-137
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• 1999

A parametric curve interpolator has been proposed for machining curves instead of a linear interpolator in which curves are approximated by a set of line segment. The parametric curve interpolator is superior to linear interpolator in machining time and contour error and generate exact position commands directly from curve equations. In this paper, a new toolpath generation method is proposed based on the parametric curve interpolator. This method retains all the benefits of parametric curve interpolator and can bound the scallop height within a specified value. By interpolating curves and surfaces directly from the mathematical equations, the amount of data from CAD/CAM system to CNC controller can be significantly reduced. The proposed method was implemented on a CNC controller and was confirmed to give a better result than the other existing method.

• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.4
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• pp.129-140
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• 1998

A numerical method is proposed to optimize automotive cam profiles. An acceleration curve of a cam follower motion is described by Hermite spline curves. Because of the intrinsic characteristics of the Hermite curve, it is possible to design an acceleration curve with arbitrary shape. Design variables in the optimization problem are location of control points which define the acceleration curve. Objective function includes dynamic performances as well as kinematic properties of a valve train. Similar optimization procedure was also performed using Polydyne cam profile synthesis method. Optimized profiles using the Hermite curve are proved to be superior to those using the Polydyne method.

• Korean Journal of Computational Design and Engineering
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• v.12 no.5
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• pp.344-353
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• 2007

In this paper, we address the problem of robust geometric modeling with emphasis on surface to surface intersections. We consider the topology and the numerical accuracy of an intersection curve to find the best approximation to the exact one. First, we perform the topological configuration of intersection curves, from which we determine the starting and ending points of each monotonic intersection curve segment along with its topological structure. Next, we trace each monotonic intersection curve segment using a validated ODE solver, which provides the error bounds containing the topological structure of the intersection curve and enclosing the exact root without a numerical instance. Then, we choose one approximation curve and adjust it within the bounds by minimizing an objective function measuring the errors from the exact one. Using this process, we can obtain an approximate intersection curve which considers the topology and the numerical accuracy for robust geometric modeling.

• The Pure and Applied Mathematics
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• v.27 no.2
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• pp.83-96
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• 2020

In this paper we study Biharmonic curves, Legendre curves and Magnetic curves in three dimensional f-Kenmotsu manifolds. We also study 1-type curves in a three dimensional f-Kenmotsu manifold by using the mean curvature vector field of the curve. As a consequence we obtain for a biharmonic helix in a three dimensional f-Kenmotsu manifold with the curvature κ and the torsion τ, κ² + τ² = -(f² + f'). Also we prove that if a 1-type non-geodesic biharmonic curve γ is helix, then λ = -(f² + f').