• 대한수학회보
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• 제53권6호
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• pp.1887-1892
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• 2016

It is well known that the helicoids are the only ruled minimal surfaces in ${\mathbb{R}}^3$. The similar characterization for ruled minimal surfaces can be given in many other 3-dimensional homogeneous spaces. In this note we consider the product space $M{\times}{\mathbb{R}}$ for a 2-dimensional manifold M and prove that $M{\times}{\mathbb{R}}$ has a nontrivial minimal surface ruled by horizontal geodesics only when M has a Clairaut parametrization. Moreover such minimal surface is the trace of the longitude rotating in M while translating vertically in constant speed in the direction of ${\mathbb{R}}$.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1997년도 춘계학술대회 논문집
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• pp.683-691
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• 1997

This paper presents a new robot trajectory generation method based on the curvatre theory of ruled surfacees. robot trajectory is represented as a ruled surface generated by the TCP (Tool center point ) and any one unit vector among the tool frame (usually denoted O, A,N). The curvature theory of ruled surfaces provides the robot control algorithm with the motion property oarameters. The proposed method eliminates the necessity of approximation technic of either joint or cartesian interpolation. This technic may give new methodology of precision robot control. Especially this is very efficient when the robot traces an analytical or form surface if the surface is geometrically modelled.

• Kyungpook Mathematical Journal
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• 제47권4호
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• pp.579-593
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• 2007

In this paper, we study some properties of ruled surfaces in a three-dimensional Lorentz-Minkowski space related to their Gaussian curvature, the second Gaussian curvature and the mean curvature. Furthermore, we examine the ruled surfaces in a three-dimensional Lorentz-Minkowski space satisfying the Jacobi condition formed with those curvatures, which are called the II-W and the II-G ruled surfaces and give a classification of such ruled surfaces in a three-dimensional Lorentz-Minkowski space.

• 호남수학학술지
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• 제28권4호
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• pp.549-558
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• 2006

In this paper, we classify non-developable ruled surfaces in a Euclidean 3-spaces satisfying some algebraic equations in terms of the second mean curvature, the mean curvature and the Gaussian curvature.

• 호남수학학술지
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• 제31권2호
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• pp.177-183
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• 2009

In this article, we study ruled surfaces in a Lorentzian space-time, which have finite type immersion. We give a condition for bi-finite type surfaces to be of finite type.

• 호남수학학술지
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• 제30권4호
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• pp.637-644
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• 2008

In this paper, we study some properties about the parallel surfaces of ruled surfaces in a Euclidean 3-space. Furthermore, we classify the parallel surfaces of ruled surfaces in a Euclidean 3-space satisfying a linear type and a quadric type with respect to the Gaussian curvature and the mean curvature.

• 호남수학학술지
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• 제46권1호
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• pp.12-37
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• 2024

The paper introduces a set of new ruled surfaces such that the base curve is taken to be the striction curve of N, C and W ruled surfaces from the alternative frame, and the generating line is taken to be one of the vectors of Sannia frame. The characterizations for each ruled surface such as fundamental forms, the Gaussian and mean curvature are also examined to provide the conditions for each surface to be developable or minimal.

• Kyungpook Mathematical Journal
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• 제62권3호
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• pp.509-531
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• 2022

In this paper we define a new family of ruled surfaces using an othonormal Sannia frame defined on a base consisting of the striction curve of the tangent, the principal normal, the binormal and the Darboux ruled surface. We examine characterizations of these surfaces by first and second fundamental forms, and mean and Gaussian curvatures. Based on these characterizations, we provide conditions under which these ruled surfaces are developable and minimal. Finally, we present some examples and pictures of each of the corresponding ruled surfaces.

• 대한수학회보
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• 제33권1호
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• pp.97-106
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• 1996

The study of surface in a Euclidean space whose Gauss map G satisfies the condition : \DeltaG = AG(*)$ for some matrix A was studied by C. Baikoussis, D. E. Blair, B. Y. Chen, F. Dillen, L. Verstraelen ([1]1, [2], [7]) and so on.

• 한국생산제조학회지
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• 제6권4호
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• pp.19-26
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• 1997

The manufacture of an impeller typically requires the 5-axis CNC machining, since the impeller is usually under working conditions such as high speed, high temperature, and high pressure. Thus, this study contributes to development of an exclusive CAM system for effective 5-axis CNC machining of a ruled surface type impeller. In this study, the sampled impeller is made of blades and a body and the blade consists of ruled surfaces between hub curve and shroud curve. In the post processing for 5-axis NC part program, the cutter axis direction vector is the straighten vector on ruled surface. The position of ball center in ball end mill cutter is decided on the interference check between the cutter and body surface of impeller using with the modified z-map method that z-axis is the same of cutter axis direction vector. The exclusive CAM system for an impeller developed in this study was very effective for designs and 50-axis machining of a ruled surface type impeller.