• 대한기계학회논문집A
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• 제24권1호
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• pp.182-189
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• 2000

This paper presents the real time control method of 5-axis NC machine for high precision and productivity based on the curvature theory, of a ruled surface. The trajectory, of NC machine is described by, way of a ruled surface generated by the points on part surface and tool axis direction vector. The curvature theory, of a ruled surface is then applied to deter-mine the motion parameters of the 5-axis machine for control. The controller computes position, orientation, and differential motion parameters of the tool in each sampling period. The real-time approach produces smoother surfaces and requires substantially less machining time compared to conventional off-line approaches. The propose real-time control method based of the curvature theory of a ruled surface may give new methodology of precision 5-axis machine control.

• 호남수학학술지
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• 제44권3호
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• pp.391-401
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• 2022

In this study, we investigate the explicit characterization of spherical curves using the Flc (Frenet like curve) frame in Euclidean 3-space. Firstly, the axis of curvature and the osculating sphere of a polynomial space curve are calculated using Flc frame invariants. It is then shown that the axis of curvature is on a straight line. The position vector of a spherical curve is expressed with curvatures connected to the Flc frame. Finally, a differential equation is obtained from the third order, which characterizes a spherical curve.

• 호남수학학술지
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• 제38권1호
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• pp.151-167
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• 2016

In Minkowskian 3-spacetime $L^3$ we find timelike or spacelike surface of revolution for the given Gauss curvature K = -1, 0, 1 and mean curvature H = 0. In fact, we set up the surface of revolution with the time axis for z-axis to be able to draw those surfaces on standard pictures in Minkowskian 3-spacetime $L^3$.

• 한국안광학회지
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• 제11권2호
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• pp.77-83
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• 2006

본 연구에서는 프리즘 처방을 위해 편심된 안경렌즈의 산각위치에 따른 수차와 경사각에 따른 수차를 계산하였다. 프리즘 처방을 위해서 일반적으로 일반 렌즈를 편심시켜 만든다. 광축과 주시축 사이의 차이는 수차를 발생시키기 때문에, 이런 경우 산각의 위치가 중요하다. 우리는 계산을 통하여 산각 회전 띠의 축이 (+)렌즈의 전면 곡률 중심을 지나는 것이 후면곡률 중심을 지나는 것보다 비점수차가 적게 발생하였고, 산각 회전 띠의 (-) 렌즈의 후면곡률 중심을 지나는 것이 전면보다 비점수차가 적게 발생한다는 결과를 얻었다. 렌즈의 굴절력이 클수록 비점수차가 작았다.

• Journal of Information Display
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• 제7권4호
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• pp.1-4
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• 2006

The optical performances of rounded prism films were investigated using a ray tracing technique. The angular distribution of the luminous intensity was obtained as functions of the prism pitch and the curvature of rounded apex and valley of prism arrays. The gain of the on-axis luminance decreased with decreasing curvature (increasing diameter) and pitch. The existence of the curved area on the prism film decreased the recycling efficiency of the prism film, i.e., the rays which would otherwise have been recycled through total internal reflections via the prism surfaces were refracted on the curved regions and redirected toward directions other than the on-axis direction. Quantitative correlation between the luminance gain and the curvature in addition to the prism pitch was obtained, which might serve as basic data for the optimization of prism films and the manufacturing processes.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 1991년도 봄 학술발표회 논문집
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• pp.81-85
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• 1991

The object of this study is to propose the bending moment-curvature relationships based on the bond properties between concrete and steel for noncraking zone, and evaluate the flexural displacement of reinforced concrete members. The bond-slip relationship and the strain hardening effect of steel were taken into account in order to evaluate the spacing of the cracks and the curvature distribution. Calculated curvature distribution along the longitudinal axis was transformed into equivalent curvature distribution. The flexural displacement was calculated by means of double intergral of the equivalent curvature. Calculated values are in good agreement with the experimental data.

• 대한수학회논문집
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• 제34권1호
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• pp.333-349
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• 2019

The paper study the curvature theory of a line-trajectory of constant Disteli-axis, according to the invariants of the axodes of moving body in spatial motion. A necessary and sufficient condition for a line-trajectory to be a constant Disteli-axis is derived. From which new proofs of the Disteli's formulae and concise explicit expressions of the inflection line congruence are directly obtained. The obtained explicit equations degenerate into a quadratic form, which can easily give a clear insight into the geometric properties of a line-trajectory of constant Disteli-axis with the theory of line congruence. The degenerated cases of the Burmester lines are discussed according to dual points having specific trajectories.

• 한국정밀공학회지
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• 제32권1호
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• pp.89-96
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• 2015

In this paper, it is studied that kinematic analysis of a 5-axis ultrasonic inspection equipment. The equipment is comprised of three straight axes and two rotary axes. With features of ultrasonic, the transmitter and receiver of the equipment are vertical to a test surface, operating at regular intervals. To perform this well, the motions of every link should be found on the based of kinematic analysis of the equipment. We chose starting point for testing and defined relations among all links through transformation of coordinates. For double curvature-shaped test object, we generated test paths. To follow these, we found motions of all links using inverse kinematics. By using Matlab/Simulink, simulator was developed, so that we could find out desired trajectories of main axes for a scan.

• Journal of Oral Medicine and Pain
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• 제21권1호
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• pp.197-206
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• 1996

This study ws performed to investigate the relationship between cervical curvature and the spatial position of the posterior part of the atlas imaged in the lateral cephalograph. Sixty six patients with temporomandibular disorders(TMD) and twenty dental students were selected for patients group and control group, respectively. The average age of patients group was 26.3 years, and 24.9 years in control group. Measured variables were cervical depth, upper space between the atlas and the base of the occiput, lower space between the atlas and the spinous process of the axis, rea of the posterior part of the atlas imaged in the lateral cephalograph, and the cervical curvature passing through the uppermost point in dorsal side of Dens of the Axis to the lowermost and rearmost point of the 5th cervical vertebra. The reliability of the method used for measuring cervical curvature with curved ruler was also tested. The results obtained were as follows : 1. Cervical depth of patients group was 122.9mm and significantly shorter than that of control group, in which cervical depth was 131.9mm, and cervical depth was significantly correlated with other variables in all subjects. 2. Upper space was greater in patients group, but total space including upper and lower space showed no difference between the two groups. The average value of total space was 26.5mm. 3. Area of the posterior part of the atlas was 168.2$\textrm{mm}^2$ in patients group, and 186.5$\textrm{mm}^2$ in control group with significant difference between the two groups. 4. Average range of radius of cervical curvature were 33-40cm and there was no difference between the two groups. 5. There was no significant correlation between the cervical curvature and the area of the posterior arch of the atlas. 6. The method using curved ruler for measuring cervical curvature could be accepted as a reliable method.

• 한국안광학회지
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• 제16권4호
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• pp.439-444
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• 2011

목적: 수평축과 수직축 비가 다른 토릭각막의 형상을 수학적인 함수로 표현하여 각막곡률 분포의 분석과 콘택트 렌즈 착용에 필요한 눈물두께 계산에 적용한다. 방법: 각막을 타원함수로 가정하고 함수로부터 유도된 곡률반경식과 각막 토포그라피 측정 곡률반경을 일치시켜 타원함수의 변수를 결정하였다. 계산은 작성한 엑셀프로그램을 사용하였다. 결과: 중심이 각막 정점에 위치하지 않는 리본(나비)형 토포그라피 이미지를 가지는 직난시 각막의 수평, 수직 각 축에 대해 각막의 형상을 수치적으로 알 수 있는 타원함수를 구하였다. 결론: 각막에 대해 고도의 수차 등이 요구되지 않는 응용, 예를 들면 콘택트렌즈 피팅, 난시교정 등에 각막 형상을 단순한 타원함수로 표현하는 것이 편리할 것으로 판단된다.