• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1339-1351
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• 2015

In this paper, using pseudo-spherical Frenet frame of pseudo-spherical curves in hyperbolic space, we define the notion of the structure functions on the non-developable ruled surfaces with timelike ruling. Then we obtain the properties of the structure functions and a complete classification of the non-developable ruled surfaces with timelike ruling in Minkowski 3-space by the theories of the structure functions.

• Journal of the Korea Computer Graphics Society
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• v.4 no.2
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• pp.69-75
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• 1998

Ruled surfaces are useful concept for surface design because they are defined by the one-parameter family of lines. In this paper, we prove that the offsets of a developable surface (a special class of ruled surfaces) are developable surfaces. Moreover, we prove that the offsets of a non-developable ruled surface cannot be ruled surfaces.

• Honam Mathematical Journal
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• v.28 no.4
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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.

• 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.