• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.301-312
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• 2015

In this paper, we study a class of spacelike rotational surfaces in the Minkowski 4-space $\mathbb{E}^4_1$ with meridian curves lying in 2-dimensional spacelike planes and having pointwise 1-type Gauss map. We obtain all such surfaces with pointwise 1-type Gauss map of the first kind. Then we prove that the spacelike rotational surface with flat normal bundle and pointwise 1-type Gauss map of the second kind is an open part of a spacelike 2-plane in $\mathbb{E}^4_1$.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.999-1013
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• 2017

In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized tractrices in Euclidean (n + 1)-space $\mathbb{E}^{n+1}$. Further, we introduce some kind of generalized rotational surfaces in Euclidean spaces $\mathbb{E}^3$ and $\mathbb{E}^4$, respectively. We have also obtained some basic properties of generalized rotational surfaces in $\mathbb{E}^4$ and some results of their curvatures. Finally, we give some examples of generalized Beltrami surfaces in $\mathbb{E}^3$ and $\mathbb{E}^4$, respectively.

• Honam Mathematical Journal
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• v.39 no.3
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• pp.363-377
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• 2017

In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized spherical curves in Euclidean (n + 1)-space ${\mathbb{E}}^{n+1}$. Further, we introduce some kind of generalized spherical surfaces in Euclidean spaces ${\mathbb{E}}^3$ and ${\mathbb{E}}^4$ respectively. We have shown that the generalized spherical surfaces of first kind in ${\mathbb{E}}^4$ are known as rotational surfaces, and the second kind generalized spherical surfaces are known as meridian surfaces in ${\mathbb{E}}^4$. We have also calculated the Gaussian, normal and mean curvatures of these kind of surfaces. Finally, we give some examples.

• Honam Mathematical Journal
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• v.38 no.2
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• pp.305-316
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• 2016

In this paper we study general rotational surfaces in the 4-dimensional Euclidean space $\mathbb{E}^4$ and give a characterization of flat general rotational surface with pointwise 1-type Gauss map. Also, we show that a flat general rotational surface with pointwise 1-type Gauss map is a Lie group if and only if it is a Clifford torus.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1863-1874
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• 2014

In this paper, we study spacelike rotational surfaces which are called boost invariant surfaces in Minkowski 4-space $\mathbb{E}^4_1$. We give necessary and sufficient condition for flat spacelike rotational surface to have pointwise 1-type Gauss map. Also, we obtain a characterization for boost invariant marginally trapped surface with pointwise 1-type Gauss map.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1345-1356
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• 2013

In this paper, we study rotational and helicoidal surfaces in Euclidean 3-space in terms of their Gauss map. We obtain a complete classification of these type of surfaces whose Gauss maps G satisfy $L_1G=f(G+C)$ for some constant vector $C{\in}\mathbb{E}^3$ and smooth function $f$, where $L_1$ denotes the Cheng-Yau operator.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.2035-2045
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• 2015

Meridian surfaces in the Euclidean 4-space are two-dimensional surfaces which are one-parameter systems of meridians of a standard rotational hypersurface. On the base of our invariant theory of surfaces we study meridian surfaces with special invariants. In the present paper we give the complete classification of Chen meridian surfaces and meridian surfaces with parallel normal bundle.

• Journal of the Korean Society of Industry Convergence
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• v.26 no.6_1
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• pp.993-999
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• 2023

In this paper, a novel polishing tool mechanism with 3-axis compliance is presented, which consists of 2-axis rotational and 1-axis linear compliances in series. The 2-axis rotational compliance mechanism is made up of four cantilever beams for adjusting rotational stiffness and one flexure universal joint at the center for constraining the z-axis deflection. The 2-axis rotational compliance can mechanically adjust the polishing tool to machined surfaces. The polishing press force can be simply controlled by using a linear spring along the z-axis. The 2-axis rotational and 1-axis linear compliance design is decoupled. The stiffness analysis of the 2-axis compliance mechanism was performed based on link compliance matrix and rigid body transformation. A 3-axis polishing tool was designed by configuring the 2-axis compliance mechanism and one linear spring.

• Korean Journal of Applied Biomechanics
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• v.14 no.2
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• pp.121-138
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• 2004

The design of soccer studs is important for providing friction on a variety of surfaces. We hypothesized that a certain type of soccer studs could improve performance due to high rotational friction. Thus, this study was conducted to determine the relationship between the frictional characteristics and different soccer stud design. Twelve recreational soccer players were recruited. Rotational friction data from the force plate was collected for all subjects during normal walking with 180 degree rotation. Walking speed was controlled at 1.2m/s (${\pm}\;0.1\;m/s$) with timing lights on infilled artificial turf. Three different types of soccer studs and one running shoe were tested. Repeated measures ANOVA was used to determine significance. Significant differences were found in rotational friction with four different shoes. Trx and World studs tended to have greater maximum rotational friction than the running shoe (Nova) and traditional soccer shoe(Copa Mondial). The results were as follow : world(25.95Nm) > trx(25.74Nm) > copa(22.50Nm) > nova(16.36Nm). The difference may be due to the number, location, size, and shape of studs. We concluded that stud design influences rotational friction between the shoe and surface during movement. Based on studs design and contact area, Trx with blade type studs are recommended since it showed high rotational friction for performance as well as enough contact area for stability. However, differences due to the mechanical properties of soccer studs are still being investigated.

• Journal of the Korean Society for Geothermal and Hydrothermal Energy
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• v.16 no.1
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• pp.1-8
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• 2020

In this study, a new shape of wind turbine with horizontal axis has been proposed. The proposed wind turbine has two pairs of 3 tiltable blades which minimizes air resistance during the reverse rotational direction. Under a given wind speed, 3D numerical simulations on tiltable blades were performed for various TSRs(tip-speed-ratios). Four cases of rotational position was considered to analyze the torque and wind power generated on the blade surfaces. The results show that the maximum wind power occurs at the TSR of 0.2. Due to the blade tilting, the wind passes through the blade without air resistance at the reverse rotational direction. The torque is mainly caused by pressure differences between the front and rear surface of the blade, and it becomes maximum when the blade is located at the azimuth angle of 330°.