• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.97-111
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• 2002

We show that an analog of the age-Grayson-Hamilton Theorem for curves moving according to their mean curvature holds for the motion of quadrilaterals according to their Menger curvature.

• The Journal of Korea Robotics Society
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• v.15 no.2
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• pp.139-146
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• 2020

In this paper, the slope of the footplate is adjusted to compensate for the centrifugal force with a series elastic actuator (SEA) attached to the Segway's body to improve the cornering characteristics during turning. To ensure Segway's driving safety in the curvature motion, it is necessary to compensate for the centripetal force by tilting the footplate to generate inward force from gravity. When the footplate is tilted under the control of SEA, the vertical load on both wheels has been changed accordingly. The frictional force of the wheel has been changed by the change of the vertical force, which requires adjustment of driving torque to keep the curvature trajectory. That is, the driving torque has been controlled to keep the curvature trajectory considering the frictional force caused by the turning motion. Four SEAs are attached to the footplate to control the slope of the footplate and the real curvature motion has been demonstrated to verify the effects of SEAs in the high- speed curvature motion.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.37-42
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• 2003

We study the asymptotic expansion in small time of the mean distance of Brownian motion on Riemannian manifolds. We compute the first four terms of the asymptotic expansion of the mean distance by using the decomposition of Laplacian into homogeneous components. This expansion can he expressed in terms of the scalar valued curvature invariants of order 2, 4, 6.

• Restorative Dentistry and Endodontics
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• v.30 no.4
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• pp.327-334
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• 2005

This study investigated the effect of anticurvature filing method on preparation of the curved root canal using ProFile. Thirty six resin blocks were divided equally into three groups by instrumentation motions: anticurvature filing motion. circumferential filing motion and straight up-and-down motion. Each resin block was sectioned at 8mm level from the apex and at the greatest curvature of the canal and reassembled in metal mold by a modified Bramante technique. All groups were instrumented with the ProFile system. At each levels. image of sectioned surface were taken using CCD camera under a stereomicroscope at $\times40$ magnification and stored. Distances of transportation at the inner and outer area of curvature and the centering ratio were determined and compared by statistical analysis. along with the assessment of the increase of root canal cross-sectional area. The results were as follows; 1. In all groups. there was no statistical difference in the mean increase of root canal cross-sectional area. the centering ratio. and the mean distances of transportation at the inner area of curvature at each level. 2. At 8mm level from the apex. the mean distances of transportation at the outer area of curvature decreases in following order anticurvature filing motion. circumferential filing motion. straight up-and­down motion but. no significant difference at the greatest curvature of the canal among three groups. Effect of anticurvature filing motion using ProFile does not seem to be different from other instrumentation motions at the inner area of curvature in curved root canal.

• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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• pp.45-48
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• 2002

Consider the mean distance of Brownian motion on Riemannian manifolds. We obtain the first three terms of the asymptotic expansion of the mean distance by means of Stochastic Differential Equation(SDE) for Brownian motion on Riemannian manifold. This method proves to be much simpler for further expansion than the methods developed by Liao and Zheng(1995). Our expansion gives the same characterizations as the mean exit time from a small geodesic ball with regard to Euclidean space and the rank 1 symmetric spaces.

• Journal of KSNVE
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• v.11 no.1
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• pp.156-166
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• 2001

This work uses tensor calculus to derive a complete set of three-dimensional field equations well-suited for determining the behavior of thick shells of revolution having arbitrary curvature and variable thickness. The material is assumed to be homogeneous, isotropic and linearly elastic. The equations are expressed in terms of coordinates tangent and normal to the shell middle surface. The relationships are combined to yield equations of motion in terms of orthogonal displacement components taken in the meridional, normal and circumferential directions. Strain energy and kinetic energy functionals are also presented. The equations of motion and energy functionals may be used to determine the static or dynamic displacements and stresses in shells of revolution, including free and forced vibration and wave propagation.

• Journal of Mechanical Science and Technology
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• v.17 no.11
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• pp.1693-1703
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• 2003

This paper presents a new local obstacle avoidance method for indoor mobile robots. The method uses a new directional approach called the Lane Method. The Lane Method is combined with a velocity space method i.e., the Curvature-Velocity Method to form the Lane-Curvature Method (LCM). The Lane Method divides the work area into lanes, and then chooses the best lane to follow to optimize travel along a desired goal heading. A local heading is then calculated for entering and following the best lane, and CVM uses this local heading to determine the optimal translational and rotational velocities, considering some physical limitations and environmental constraint. By combining both the directional and velocity space methods, LCM yields safe collision-free motion as well as smooth motion taking the physical limitations of the robot motion into account.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.482-487
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• 2002

This paper presents a robot trajectory generation method based on the dual curvature theory of ruled surfaces. Robot trajectory can be represented as a ruled surface generated by the TCP(Tool Center Point) and my unit vector among the tool frame. Dual curvature theory of ruled surfaces provides the robot control algorithm with the motion property parameters. With the differential properties of the ruled surface, the linear and angular motion properties of the robot end effector can be utilized in the robot trajectory planning.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.3
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• pp.313-320
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• 1999

The Lane-Curvature Method(LCM) presented in this paper is a new local obstacle avoidance method for indoor mobile robots. The method combines Curvature-Velocith Method(CVM) with a new directional method called the Lane Method. The Lane Method divides the environment into lanes taking the information on obstacles and desired heading of the robot into account ; then it chooses the best lane to follow to optimize travel along a desired heading. A local heading is then calculated for entering and following the best lane, and CVM uses this heading to determine the optimal translational and rotational velocity space methods, LCM yields safe collision-free motion as well as smooth motion taking the dynamics of the robot Xavier, show the efficiency of the proposed method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.9
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• pp.2223-2236
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• 1995

0The fields of turbomachinery and electrical generators provide many examples of flow through rotating internal passages. At the practicing Reynolds number, most of the flow motion is three dimensional and highly turbulent. The proper understanding for the characteristics of these turbulent flow is necessary for the design of thermo-fluid machinery of a good efficiency. The flow characteristics in the rotating duct with curvature are very complex in practice due to the curvature and rotational effect of the duct. The understanding of the effect of the curvature on the structure and rotational effect of the duct. The understanding of the effect of the curvature on the structure of turbulence in the curved passage and the characteristics of the flow in a rotating radial straight channel have been well studied separately by many workers. But the combined effects of curvature and rotation on the flow have not been well understood inspite of the importance of the phenomena in the practical design process. In this study, the characteristics of a developing turbulent flow in a square sectioned 90.deg. bend rotating at a constant angular velocity are measured by using hot-wire anemometer to seize the rotational effects on the flow characteristics. As the results of this study, centrifugal forces associated with the curvature of the bend and Coriolis forces and centripetal forces associated with the rotational affect directly both the mean motion and the turbulent fluctuations.