• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.347-348
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• 2006

Among various gear system, planetary gear system has the best characteristics in high efficiency, excellent strength capacity, easy convertible speed control, and compact design aspect. Strength of gear is considered as the most important design factor. We have studied tooth form and the planetary gear system that have high reduction gear ratio is created by using the involute curve.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1142-1147
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• 2004

The tooth profile of helical gear that is manufactured by the rack cutter consists of the involute curve and the trochoid curve. However, gear designers are very hard to calculate the exact profile because it needs very complex information about the gear manufacturing. Therefore, the purpose of this study is to develop the automatic generation program for the helical gear using the Solid Works API. First, involute and trochoide coordinates by the rack cutter are calculated. Using the data, Visual Basic program for the helical gear model is coded. This work gives us the quick helical gear modeling and can be used as the modeling for the finite element analysis.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.4
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• pp.129-135
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• 1996

The area of gear vibration and noise, has recently been the focus of many studies. The proper kinematic and geometric design of gears, the mathematical modeling of gear system are essential for a good design. This work present a gear disign for reducing noise, and practical approaches used for machinery noise reduction slong with the summary of methods available for predicting gear noise in terms of the transmis- sion error, and show a comparative study with other methods. A new tooth profile modification is proposed for reducing vibration and noise of involute gears. The method is based on the use of cubic spline curves. The tooth profile is constrained to assume an involute shape during the loaded operation. Thus the new gear profile assures conjugate motion at all points along the line of action. The new profile is found to result in a more uniform static transmission error compared to not only standard involute profile but also modificated profile therby contributing to the improvement of vibration and noise characteristics of the gear.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.05a
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• pp.600-603
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• 2002

In this study, Automatic design program creates 3D solid models and constructs them. The method of making assembly model is two. One assembles the element made in automatic design program with hand, the other develops the automatic design program fur creating assembly model. Automatic design program improves the convenience of user. In creating gears, involute curve and Trochoidal fillet curve are made by mathematical development.

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.117-135
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• 2018

The orthogonal trajectories of the first tangents of the curve are called the involutes of x. The hyperspheres which have higher order contact with a curve x are known osculating hyperspheres of x. The centers of osculating hyperspheres form a curve which is called generalized evolute of the given curve x in n-dimensional Euclidean space ${\mathbb{E}}^n$. In the present study, we give a characterization of involute curves of order k (resp. evolute curves) of the given curve x in n-dimensional Euclidean space ${\mathbb{E}}^n$. Further, we obtain some results on these type of curves in ${\mathbb{E}}^3$ and ${\mathbb{E}}^4$, respectively.

• Transactions of Materials Processing
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• v.3 no.1
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• pp.97-109
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• 1994

Closed-die forging of the spur gears with circular are fillet has been analyses by using the upper-bound method. A kinematically admissible velocity field has been developed, wherein, the tooth profile consists of the involute curve and the circular arc fillet. In the analysis, the deformation regions have been divided into eight zones. A constant frictional stress has been assumed on the contacting surfaces Utilizing the formulated velocity field, numerical calculations have been carried out to investigate the effects of various parameters, such as module, number of teeth, addendum modification coefficient and friction factor, on the relative forging pressure of spur gears. As the result of numerical calculations, the relative forging pressure does not change so much against the variation of module. On the other hand, the relative forging pressure increases at the final filling stage as the addendum modification coefficient increases.

• Journal for History of Mathematics
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• v.28 no.1
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• pp.31-44
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• 2015

The cycloid curve had been studied by many mathematicians in the period from the 16th century to the 18th century. The results of those studies played important roles in the birth and development of Analytic Geometry, Calculus, and Variational Calculus. In this period mathematicians frequently used the cycloid as an example to apply when they presented their new mathematical methods and ideas. This paper overviews the history of mathematics on the cycloid curve and presents proofs of its important properties.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.10a
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• pp.257-258
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• 2006

• Tribology and Lubricants
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• v.30 no.4
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• pp.212-217
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• 2014

A counter gear transmits the rotation angle, so the angular velocity ratio of the gear does not necessarily need to be constant in the meshing process. As a pinion has a small number of teeth when combined with an internal gear for counters, tooth interference can occur with the use of an involute curve. This paper introduces circular arcs that represent a tooth profile and fillet for the profile design of a pinion through the combination of arcs with lines. The straight line of a rack tooth represents the profile of a mating internal gear. Thus, the circular arc and line maintain contact during the rotation of the counter gear. This paper presents an analysis of the meshing of the circular arc tooth and rack tooth along with the properties of the counter gear, such as the change in rotational velocity and amount of backlash. The contact ratio of the counter gear is 1 because the tooth contact occurs between circular arcs and line. The initial position of tooth contact, which denotes the simultaneous contact of two teeth, is found. As the rotation of the pinion, only one tooth keeps the contact situation. This meshing property is analyzed by the geometrical constraints of the tooth profile in contact and the results are presented as graphical diagrams in which tooth-arc movements are superimposed.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.2
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• pp.102-112
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• 1997

This paper describes the method that can construct kinematically admissible velocity fields for forging of gear-like components which have tooth shape around the cylinder. The kinematically admissible velo- city fields for the various gear-like components, involute spur gear, trapezoidal spline, square spline, ser- ration and trochoidal gear, were constructed by pilling up the velocity components according to the shape of tooth and billet. The billets, of hollow and solid, were Al 2218 and 2024. To verify the method, the analyses and experiments were carried out and compared with each other. For analyses, the half pitches of com- ponents were divided into several deformation regions based on their tooth profile. A neutral surface was used to represent the inner flow of material during forging. Its location varied with the energy optimazation and its contour varied with the number of teeth. In experiment, the contour of material filling up the tooth zone is hyperbolic curve caused by the frictional drag on the interface of die-wall/workpiece but, in the analysis, it is an arc which retains the same contour during all forging operation.