• Bulletin of the Society of Naval Architects of Korea
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• v.27 no.3
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• pp.11-18
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• 1990

The Kelvin's method of stationary phase breaks down at the cusp point and yields a nonuniform expansion near it. By making use of the nonuniform expansion, we derive a uniform expansion near the cusp point.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.10a
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• pp.106-110
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• 2001

The ball-end milling process is widely used in the die/mold industries, and it is very suitable for the machining of free-form surfaces. However, this process is inherently inefficient process to compared with the end-milling or face milling process, since it relays upon the machining at the cutter/surface contact point. The machined part is the result of continuous point-to-point machining on the free-form surface. And cusps (or scallops) remain at the machined part along the cutter paths and they give the geometrical roughness of the workpiece. Thus, for the good geometrical roughness of the workpiece, it is required very tightly spaced cutter paths in this ball-endmilling process. However, with the tight cutter paths, the geometrical roughness of the workpiece is not regular on the workpiece since the cusp height is variable in the previously developed ISO-parametric or Cartesian machining methods. This paper suggests a method of tool path generation which makes the geometrical roughness of workpiece be constant through the machined surface. In this method, Ferguson Surface design Model is used and cusp height is derived from the instantaneous curvatures. And, to have constant cusp height, an increment of parameter u or v is estimated along the reference cutter path. In ball-end milling experiments, the cusp pattern was examined, and it was proved that the geometrical roughness could be regular by suggested tool path generation method.

• International Journal of CAD/CAM
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• v.7 no.1
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• pp.21-30
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• 2007

The inverse offset method (IOM) is widely used for generating cutter paths from the point-based surface where the surface is characterised by a set of surface points rather than parametric polynomial surface equations. In the IOM, cutter path planning is carried out by specifying the grid sizes, called the step-forward and step-interval distances respectively in the forward and transverse cutting directions. The step-forward distance causes the chordal deviation and the step-forward distance produces the cusp. The chordal deviation and cusp are also functions of local surface slopes and curvatures. As the slopes and curvatures vary over the surface, different step-forward and step-interval distances are appropriate in different areas for obtaining the machined surface accurately and efficiently. In this paper, the chordal deviation and cusp height are calculated in consideration with the surface slopes and curvatures, and their combined effect is used to estimate the machined surface error. An adaptive grid generation algorithm is proposed, which enables the IOM to generate cutter paths adaptively using different step-forward and step-interval distances in different regions rather than constant step-forward and step-interval distances for entire surface.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.05a
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• pp.944-947
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• 2000

Sculptured surface machining plays a vital role in the process of bring new products to the market place. A great variety of products rely on this technology for the production of the dies and moulds used in manufacturing. And, the use of CNC machines and CAD/CAM system has become a vital parts of product development process. The propose of this study is to investigate the effect of cutting parameters on the machinability such as surface roughness and cusp generated in the machining of sculptured surface on a three-axis CNC machining center using the CAD/CAM system. Experimental result showed that: In step down cutting, as the inclined angle of surface became smaller, the cusp height appeared higher. On the other hand, in step over cutting, as the inclined angle of surface became larger, the cusp height appeared higher. In the point of precision machining, step over cutting was more effective. For the minimization of cusp height, step down cutting was effective in larger inclined surface, but step over cutting in smaller inclined surface.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.147-155
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• 1999

Let {$C_t$} be a pencil of smooth quartics for $t{\neq}0$ degenerating to a plane quartic $C_0$ with an ordinary cusp of multiplicity 3. We compute the stable limit as $t{\rightarrow}0$ of {$C_t$} when the total surface of this family has a triple point at the singular point of $C_0$.

• Proceedings of the Korean Printing Society Conference
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• 2002.05a
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• pp.10-18
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• 2002

On the process of cross-media color reproduction, a key feature is the use of gamut mapping techniques to adjust the different color gamuts between displays and printers. Even though a number of GMAs have been published, but there are no method satisfactory enough for more exect color reproduction. In this paper, the gamut mapping methods of nearest point clipping(NPC), centroid clipping (SLIN), straight clipping and cusp clipping(CUSP) were tested and analyzed with color difference, and a new gamut mapping algorithm based on variable anchor point method was proposed.

• Journal of Oral Medicine and Pain
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• v.19 no.1
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• pp.57-72
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• 1994

This study was undertaken to obtain the data age determination following the eruption of individual cusps of the first molars in the point of forensic odontology. 532 children (294 male and 238 female, born between April, 1989 and March, 1986) from a kindergarten and a primary school in a reesidential district in Seoul were studied. The eruption state of the first molar was divides into 6 stages according to the degree of exposure of individual cusps, and correlation between the stage and age was stastically analysed. The results of the study lead to following conclusions : 1. The most frequently seen eruption sequence of cusps for the upper first molar was mesibuccal cusp, mesiopalatal cusp, distobuccal cusp, mesiodistal cusp, distopalatal cusp. As for the lower first molar : mesiobuccal cusp, mcsiolingual cusp, distobuccal cusp, distolingual cusp. 2. The time of eruption was earlier in the female ethan in the male, but it was stastically remarkable only in upper and lower parts of the right and the left teeth of subjects age between 6.0 and 6.5 and upper part of the right and the left teeth of subjects age over 7.5 3. The eruption of the lower first molar was comparatively earlier than that of the upper first molar and there was no significant stastical difference between the right and the left first molars in the time of eruption. 4. There was no noticeable difference in the eruption sequence of cusps, irrespective of sex and side. 5. The eruption of the upper first molar is started at the age of about 6.4 and complete the age of about 7.1 and as for the lower first molar, it is from 6.3 to 7.0

• The korean journal of orthodontics
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• v.26 no.5 s.58
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• pp.535-546
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• 1996

The purpose of this study was to classify mandibular dental arch forms based on Raberin's method, and to compare Raberin's arch forms with that of the Korean's, and to designate arch form of bracket level according to distance between cusp tip and buccal surface of bracket level. The sample consisted of 159 mandibular dental casts showing normal occlusion which was taken from 62 males and 97 females of the Korean, aging from 13 to 25 years. The model was taken by X-ray. The landmarks were cusp points which expressed the mandibular dental arch line of cusp tips and buccal points which were measured from cusp tips to buccal surfaces of bracket level. The landmarks on the film were digitized, and measurements and statistics were performed. The results were as follows; 1. The models were classified as type 1, type 2, type 3, type 4 and type 5 by the author, and polynomial functions of the six degree and R-square values were calculated using statistical method, and each calculated equations explained each group with the least R-square value of 0.97, and each arch forms' were plotted. 2. The distribution of type 1 was $17.6\%$, type 2 $20.8\%$, type 3 $20.8\%$, type 4 $16.3\%$ and type 5 $24.5\%$. 3. The Korean arch form was characterized by larger width, smaller height compared to the French arch form. 4. The designated arch form of bracket level, viz the distance between cusp point and buccal point was calculated. The distance between cusp point and buccal point of incisor was 1mm, canine 1.9mm, first premolar 2.5mm, second premolar 2.6mm, first molar 2.7mm and second molar 2.7mm.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.339-350
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• 2006

The bifurcation point where a satellite component buds from another component is characterized by the existence of the common tangent line between the two osculating components appearing in the degree-n bifurcation set. We investigate the existence, location and number of bifurcation points for satellite components budding from the main component in the degree-n bifurcation set as well as a parametric boundary equation of the main component of the degree-n bifurcation set. Cusp points are also located on the boundary of the main component. Typical degree-n bifurcation sets and their components are illustrated with some computational results.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.2
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• pp.43-57
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• 2003

The boundary of a typical period-2 component in the degree-3 bifurcation set is formulated by a parametrization of its image which is the unit circle under the multiplier map. Some properties on the geometry of the boundary are investigated including the root point, the cusp and the length as well as the area bounded by the boundary curve. The centroid of the area for the period-2 component was numerically found with high accuracy and compared with its center. An algorithm drawing the boundary curve with Mathematica codes is proposed and its implementation exhibits a good agreement with the analysis presented here.