• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.1 s.173
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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.

• Honam Mathematical Journal
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• v.44 no.3
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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.

• Honam Mathematical Journal
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• v.38 no.1
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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 $L^3$.

• Journal of Korean Ophthalmic Optics Society
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• v.11 no.2
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• pp.77-83
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• 2006

We have studied the astigmatism according to the bevel position and the tilting(pantoscopic) angle of decentered spectacle lens for prism prescription. For prism prescription, generally we make a general spectacle lens into decentered spectacle lens. At this time the bevel position of decentered lens is a important matter, because the difference between optic axis and visual axis occur aberrations. Using the calculation we find that the case that the axis of bevel rotation band passes the front curvature center of (+) lens has a smaller astigmatism than the case that the axis of bevel rotation band passes the rear curvature center of (+) lens and that the case that the axis of bevel rotation band passes the rear curvature center of (-) lens has a smaller astigmatism than the case that the axis of bevel rotation band passes the front curvature center of (-) lens. We find the lens with higher refraction index has a smaller astigmatism.

• Journal of Information Display
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• v.7 no.4
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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.

• Proceedings of the Korea Concrete Institute Conference
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• 1991.04a
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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.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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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.

• Journal of the Korean Society for Precision Engineering
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• v.32 no.1
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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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• v.21 no.1
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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.

• Journal of Korean Ophthalmic Optics Society
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• v.16 no.4
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• pp.439-444
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• 2011

Purpose: To represent the shape of toric corea in the elliptical function for the determination of curvature distribution and lacrimal thickness between cornea and contact lens when the lens is fitted. Methods: Topography measurements of corneal curvature and curvature equation derived from the assumed elliptical function were evaluated using the Excel program which included the necessary equation derived. Results: Mathematical expressions for the cornea whose ribbon shaped-topography image, in which the center does not coincide with the corneal apex, can be determined. Conclusions: For the application where the higher accuracy on the cornea is not required, such as higher order aberration, the cornea cal be expressed in the simple elliptical function.