• 한국수학교육학회:학술대회논문집
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• 한국수학교육학회 2010년도 제44회 전국수학교육연구대회
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• pp.145-150
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• 2010

• 한국수학사학회지
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• 제28권1호
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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.

• 한국공작기계학회논문집
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• 제11권3호
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• pp.80-85
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• 2002

The free curve gear is a non-circular gear without any relating center, which can perform free curve motion for complicated mechanisms, and minimize the work area. In this study, an algorithms for tooth profile generation of free curve involute gear is developed. The algorithm uses the involute gear creating principle in which a gear can be generated by rolling with another standard involute one. Cycloid me and third polynomial curve gears were designed and verified by computer graphics. These gears are manufactured in the wire-cut EDM and examined in engagement with a standard spur gear. The results showed that the proposed algorithm is successful to design and to manufacture the free curve gear with concave and convex profiles.

• 대한기계학회논문집A
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• 제35권3호
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• pp.241-250
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• 2011

본 논문에서는 하이포 및 에피 사이클로이드 곡선 사이에 원호 곡선을 삽입하여 내부로터를 설계하고 로터 회전시뮬레이션 및 간섭회피를 위한 수정법을 통해 외부로터를 설계하는 방식의 제로터를 개발하였다. 또한 접촉점을 이용한 기존의 유량계산법을 사용할 수 없는 경우에 유량 및 유량맥동을 도출할 수 있는 챔버면적 계산법을 개발하였다. 이와 같은 방식의 제로터는 로터 설계시 첨점 및 루프가 발생하지 않으며, 내부로터의 하이포 사이클로이드 및 원호 곡선 연결점에서 새로운 설계변수인 경사각 $\gamma$가 추가되어 편심량 설정시 첨점 및 루프 발생 방지조건 또는 이끝폭의 설계 한계조건으로부터 제한을 받지 않는다. 따라서 설계자는 편심량 및 각도 $\gamma$를 조절함으로써 실제 산업현장에서 보다 효과적으로 로터 최적설계를 수행할 수 있다.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2006년도 춘계학술대회 논문집
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• pp.389-390
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• 2006

The cycloidal reducer is one of the velocity controlling equipments in machinery. It has advantages of the higher reduction ratio, the higher accuracy, the easier adjustment of the transmission ratio and the smaller workspace than any other kinds of the reducers. This paper proposes a simple and exact approach for the lobe profile design of the two teeth difference cycloidal plate gear, which is different from the standard cycloidal reducer, by means of the principle of the instant velocity center in the general contact mechanism and the homogeneous coordinate transformation.

• 한국정밀공학회지
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• 제16권9호
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• pp.48-53
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• 1999

In this paper, a practical method for design and machining of cycloid gear was investigated. Based on the proposed method, a systematic program was developed for automatically designing the tooth profiles of epicycloid and hypocycloid gears for the case fo one difference between the number of teeth of cycloid gear and the number coordinates of tooth profiles and pressure angles. The error analysis between cycloid curve and Biarc curve was performed to show the effective method of equidistant partitioning of cycloid curve so that efficient method of Biarc curve fitting was also proposed for the partitioned curve.

• East Asian mathematical journal
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• 제26권4호
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• pp.447-461
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• 2010

Papert [17] introduced the LOGO environment in which we make a curve using LOGO commands (FORWARD, ROTATE). We call this geometry as turtle geometry. This environment has influenced many researchers and designers of computers and mathematics education. But the curve that we can make using LOGO command is elementary or too difficult. Polygon and circle is elementary and making other curves is difficult. In this paper, we introduce the method of drawing some other curves mediating new command. First, we study epicycloid and hypocycloid in the historical and the physical context. And we introduce the method of making epicycloid and hypocycloid using vector addition. Next we study the polygon patterns of this curve. Finally, we extend the method for making more general curve and we improve the computer environment using this metaphor.

• 한국정밀공학회지
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• 제29권9호
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• pp.1003-1011
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• 2012

A new type of gerotor developed in this paper has the inner rotor designed by inserting a polycircular-arc between the hypocycloid and epicycloid curves, and we also suggest that the outer rotor be designed using the closed-form equation for the inner rotor and a method of modification. Thus, it is possible to design a gerotor for which there is no cusp and loop, as in this case undercut is prevented. We developed automated program for rotor design and calculation of the flow rate and flow rate irregularity. And we also demonstrate the superior performance of the gerotor developed in this study by analyzing the internal fluid flow using a commercial computation fluid dynamics-code (CFD).

• 한국기계가공학회지
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• 제3권2호
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• pp.46-52
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• 2004

The most of reducers consist of many gear parts, but a ball reducer never contains a gear. As the ball reducer with gearless has no back lash, it is necessary more and more to precision machine. The reducing of ball reducer happens by cycloid curves and all instant relative velocity centers always pass on a given constant position when rotational running. Then, it is difficult to calculate cycloid curve for design and machining. So, this paper studied a software for the design of the ball reducer design and machined all parts included among cycloid curve. By using the developed software, this study has large benefit to design every ball reducer.

• 한국수학교육학회지시리즈A:수학교육
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• 제53권3호
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• pp.313-327
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• 2014

'Tangent' is one of the most important concepts in the middle and high school mathematics, especially in dealing with calculus. The concept of tangent in the current textbook consists of the ways which make use of discriminant or differentiation. These ways, however, do not present dynamic view points, that is, the concept of variation. In this paper, after applying 'Roberval's way of finding tangent using vectors in terms of kinematics to parabola, ellipse, circle, hyperbola, cycloid, hypocycloid and epicycloid, we will identify that this is the tangent of those curves. This trial is the educational link of mathematics and physics, and it will also suggest the appropriate example of applying vector. We will also help students to understand the tangent by connecting this method to the existing ones.