• Kyungpook Mathematical Journal
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• v.57 no.1
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• pp.133-144
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• 2017

In this paper, we study ruled surfaces in 3-dimensional Euclidean and Minkowski space in terms of their Gauss map. We obtain classification theorems for these type of surfaces whose Gauss map G satisfying ${\Box}G=f(G+C)$ for a constant vector $C{\in}{\mathbb{E}}^3$ and a smooth function f, where ${\Box}$ denotes the Cheng-Yau operator.

• Korean Journal of Mathematics
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• v.32 no.2
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• pp.259-284
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• 2024

In present study, we introduce ruled surfaces whose base curve is the Salkowski curve in Euclidean 3-space and whose generating lines consist of the Frenet vectors of this curve (tangent, principal normal and binormal vectors). Then, we produce regular surfaces from a vector with real coefficients, which is a linear combination of these vectors, and we examine some special cases for these surfaces. Moreover, we present some geometric properties and graphics of all these surfaces.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.3
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• pp.83-90
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• 2004

This paper proposes a tool path generation method for machining impellers with 5-axis machining center. The shape of impeller is complex, being composed of pressure surface, suction surface and leading edge, and so on. The compound surface which is made of ruled surface such as pressure surface and suction surface and leading edge such as fillet surface, makes the tool path generation much complicated. To achieve efficient roughing, cutting area is divided into two region and then tool radius of maximum size that do not cause tool intereference is selected for shortening machining time. In finishing, accuracy is improved using side cutting for blade surface and point milling for leading edge.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.235-239
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• 2001

Finding intersection point between a surface and a line is one of major problem in CAD/CAM. The intersection point could be found in an exact form or with numerical method. In this paper, the exact solution of the intersection point between a ruled surface which is generated by the movement of an endmill and the z-direction vector is presented. The cutter swept surface which is a ruled surface and the Z-direction vector are represented with parametric equations. With the nature of parametric equations, the geometric properties at the intersection point are easily acquired.

• Honam Mathematical Journal
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• v.41 no.4
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• pp.683-695
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• 2019

In the present paper, we study curves in 𝔼³ with density $e^{ax^2+by^2}$, where a, b ∈ ℝ not all zero constants and give the parametric expressions of the curves with vanishing weighted curvature. Also, we create ruled surfaces whose base curves are the curve with vanishing weighted curvature and the ruling curves are Smarandache curves of this curve. Then, we give some characterizations about these ruled surfaces by obtaining the mean curvatures, Gaussian curvatures, distribution parameters and striction curves of them.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2000.10a
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• pp.175-180
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• 2000

This paper describes the method and the process for impeller machining on 5-axis CNC machining center. Also, The CAD/CAM software for the impeller post processing is developed. The software can be interfaced with Solid-works software for confirmation of the impeller shapes. In this study, blades on impeller is described from Ruled-surfaces between two Ferguson curves. In this study, using 5-axis NC part program obtained from the developed software, a sample impeller was machined on 5-axis CNC machining center. The machined impeller was very agreeable to the designed impeller. Thus, theories proposed in this study can be very useful for the 5-axis machining of impeller blades with Ruled-surfaces.

• Transactions of Materials Processing
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• v.29 no.3
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• pp.144-150
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• 2020

In this paper, we propose the generation of a double enveloping worm thread profile with a non-developable ruled surface. Thread surface machining cuts all the way from the tip to the tooth root at one time, like full-face contact machining, rather than cutting several times like point machining. This cutting can reduce the cutting duration and achieve the smooth surface that does not require a grinding process for the threaded surface. The mathematical model of the cutting process was developed from theoretical equations, and the tooth surface was generated using two parameters and modeled in the CATIA using the generated Excel data. Additionally, the machining process of the worm was simulated in a numerical control simulation system. To verify the validity of the proposed method, the deviation between the modeling and the workpiece was measured using a 3D measuring machine.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.957-971
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• 2020

In this paper, we introduce a new method to construct a parametric surface in terms of curves and points lying on Euclidean 3-space, called a C⁰-Hermite surface interpolation. We also prove the existence of a C⁰-Hermite interpolation of isoparametric surfaces with the so-called marching scale functions, and give some examples. Finally, we construct ruled surfaces and surfaces foliated by a circle as an isoparametric surface.

• Korean Journal of Mathematics
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• v.25 no.4
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• pp.513-535
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• 2017

As a continuation to the study in [8, 12, 15, 17], we construct bi-conservative central normal (BCN) and bi-conservative asymptomatic normal (BAN) ruled surfaces in Euclidean 3-space ${\mathbb{E}}^3$. For such surfaces, local study is given and some examples are constructed using computer aided geometric design (CAGD).

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.568-571
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• 2004

This paper presents an efficient 5-axis roughing method for centrifugal impeller. The efficient roughing is minimization of cutting time through minimizing tool tilting & rotating motions. Roughing tool path plan consists of the three steps. First, machining areas are divided into sub cutting regions using ruling lines. The biggest tool diameter is, then, determined for each region. Finally, tool paths are generated after fixing the tilting and rotating axis of 5-axis machine. Experimental results showed that the proposed roughing plan considering the divided machining regions is more efficient than the conventional methods.