• Journal of the Korean Society for Precision Engineering
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• v.29 no.10
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• pp.1119-1127
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• 2012

In this paper, we present an inverse kinematics of a 7-dof Anthropomorphic robot arm using conformal geometric algebra. The inverse kinematics of a 7-dof Anthropomorphic robot arm using CGA can be computed in an easy way. The geometrically intuitive operations of CGA make it easy to compute the joint angles of a 7-dof Anthropomorphic robot arm which need to be set in order for the robot to reach its goal or the positions of a redundant robot arm's end-effector. In order to choose the best solution of the elbow position at an inverse kinematics, optimization techniques have been proposed to minimize an objective function while satisfying the euler-lagrange equation.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.670-673
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• 2000

This paper attempt analysis and computer simulation of dynamics of a set of dual multi-joint fingers with soft-deformable tips which are grasping. Firstly, a set of differential equation describing dynamics of the fingers and object together with geometric constraint of tight area-contacts is formulated by Euler-Lagrange's formalism. Secondly, problems of controlling both the internal force and the rotation angle of the grasped object under the constraints of area-contacts of tight area-contacts are discussed. The effect of geometric constraints of area-contacts on motion of the overall system is analyzed and a method of computer simulation for overall system of differential-algebraic equations is presented. Finally, simulation results are shown and the effects of geometric constraints of area-contact is discussed.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.224-229
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• 1997

This paper compares the control techniques for position control experiments of a fixible robot moving in a vertical plane. The flexible manipulator is modeled as an Euler-beroulli beam. Elastic deformantion is representedusing the assumed model method. A comparison function which satisfies all geometric and natural boundary conditions of a cantilever beam with an end mass is used as an assumed mode shape. Lagrange's equation is utilized for the development of a discretized model. Control schemes are developed using PID control,pole placement control and discrete Linear Quadratic Regulater(LQQ). The effectiveness of the developed control schems are compared using computer simulation in view of practical experiment. The simulation results show that PID control is very effective in practical implementation.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.211-214
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• 1995

Let M and N be compact Riemannian manifolds and $f : M \to N$ be a smooth map. Following J. Eells, f is exponentially harmonic if it represents a critical point of the exponential energy integral $$ E(f) = \int_{M} exp(\left\$\mid$ df \right\$\mid$^2) dM $$ where $(\left\ df $\mid$\right\$\mid$^2$ is the energy density defined as $\sum_{i=1}^{m} \left\$\mid$ df(e_i) \right\$\mid$^2$, m = dimM, for orthonormal frame $e_i$ of M. The Euler- Lagrange equation of the exponential energy functional E can be written $$ exp(\left\$\mid$ df \right\$\mid$^2)(\tau(f) + df(\nabla\left\$\mid$ df \right\$\mid$^2)) = 0 $$ where $\tau(f)$ is the tension field along f. Hence, if the energy density is constant, every harmonic map is exponentially harmonic and vice versa.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2004.03a
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• pp.186-191
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• 2004

The reactive flowfield of the transverse injecting combustor has been studied using Euler-Lagrange method in order to develop an efficient solution procedure for the understanding of liquid spray combustion in the transverse injecting combustor which has been widely used in ramjets and turbojet afterburners. The unsteady two-dimensional gas-phase equations have been represented in Eulerian coordinates and the liquid-phase equations have been formulated in Lagrangian coordinates. The gas-phase equations based on the conservation of mass, momentum, and energy have been supplemented by combustion. The vaporization model takes into account the transient effects associated with the droplet heating and the liquid-phase internal circulation. The droplet trajectories have been determined by the integration of the Lagrangian equation in the flow field obtained from the separate calculation without considering the iterative effect between liquid and gas phases. The reported droplet trajectories had been found to deviate from the initial conical path toward the flow direction in the very end of its lifetime when the droplet size had become small due to evaporation. The integration scheme has been based on the TEACH algorithm for gas-phase equation, the second order Runge-Kutta method for liquid-phase equations and the linear interpolation between the two coordinate systems. The calculation results has shown that the characteristics of the droplet penetration and recirculation have been strongly influenced by the interaction between gas and liquid phases in such a way that most of the vaporization process has been confined to the wake region of the injector, thereby improving the flame stabilization properties of the flowfield.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.1
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• pp.1-9
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• 2013

This paper presents a new control algorithm for dynamic control of a unicycle robot. The unicycle robot motion consists of a pitch that is controlled by an in-wheel motor and a roll that is controlled by a reaction wheel pendulum. The unicycle robot doesn't have any actuator for a yaw axis control, which makes the derivation of the dynamics relatively simple. The Euler-Lagrange equation is applied to derive the dynamic equations of the unicycle robot to implement the dynamic speed control of the unicycle robot. To achieve the real time speed control of the unicycle robot, the sliding mode control and LQ regulator are utilized to guarantee the stability while maintaining the desired speed tracking performance. In the roll controller, the sigmoid-function based sliding mode controller has been adopted to minimize the chattering by the switching function. The LQR controller has been implemented for the pitch control to drive the unicycle robot to follow the desired velocity trajectory in real time using the state variables of pitch angle, angular velocity, angle and angular velocity of the wheel. The control performance of the two control systems form a single dynamic model has been demonstrated by the real experiments.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.5 s.98
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• pp.620-628
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• 2005

In this paper, we studied about the dynamic behavior of a cracked rotating cantilever beam. The influences of a rotating angular velocity, the crack depth and the crack position on the dynamic behavior of a cracked cantilever beam have been studied by the numerical method. The equation of motion is derived by using the Lagrange's equation. The cracked cantilever beam is modeled by the Euler-Bernoulli beam theory. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. The lateral tip-displacement and the axial tip-deflection of a rotating cantilever beam is more sensitive to the rotating angular velocity than the depth and position of crack. Totally, as the crack depth is increased, the natural frequency of a rotating cantilever beam is decreased in the first and second mode of vibration. When the crack depth is constant, the natural frequencies of a rotating cantilever beam are proportional to the rotating angular velocity in the each direction.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.5 s.98
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• pp.586-594
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• 2005

In this paper, we studied about the effects of the rotating cantilever pipe conveying fluid with a moving mass. The influences of a rotating angular velocity, the velocity of fluid flow and moving mass on the dynamic behavior of a cantilever pipe have been studied by the numerical method. The equation of motion is derived by using the Lagrange's equation. The cantilever pipe is modeled by the Euler-Bernoulli beam theory. When the velocity of a moving mass is constant, the lateral tip-displacement of a cantilever pipe is proportional to the moving mass and the angular velocity. In the steady state, the lateral tip-displacement of a cantilever pipe is more sensitive to the velocity of fluid than the angular velocity, and the axial deflection of a cantilever pipe is more sensitive to the effect of a angular velocity. Totally, as the moving mass is increased, the frequency of a cantilever pipe is decreased in steady state.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.7
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• pp.562-569
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• 2003

An iterative modal analysis approach is developed to determine the effect of transverse open cracks on the dynamic behavior of simply supported pipe conveying fluid subject to the moving mass. The equation of motion Is derived by using Lagrange’s equation. The influences of the velocity of moving mass and the velocity of fluid flow and a crack have been studied on the dynamic behavior of a simply supported pipe system by numerical method. The presence of crack results In higher deflections of pipe. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. Totally. as the velocity of fluid flow and the crack severity are increased, the mid-span deflection of simply supported pipe conveying fluid Is Increased. The time which produce the maximum dynamic deflection of the simply supported pipe Is delayed according to the increment of the crack severity.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.387-394
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• 2000

Theoretical and experimental study is conducted on the contact pressure distribution of a radial tire in motion under various camber angles. Tire construction is modelled by a spring bedded elastic ring, consisted of sidewall springs and a composite belt ring. The contact area is assumed to be a trapezoidal shape varying with camber angles and weighted load. The basic equation in a quasi-static form is derived for the deformation of a running belt with a constant velocity by the aid of Lagrange-Euler transformation. Galerkin's method and stepwise calculation are applied for solving the basic equation and the mechanical boundary condition along both sides of the contact belt part subjected to shearing forces transmitted from the sidewall spring. Experimental results on the contact pressure, measured by pressure sensors embedded in the surface of the drum tester, correspond well with the calculated ones for the test tire under various camber angles, running velocities and weighted loads. These results indicate that a buckling phenomenon of the contact belt in the widthwise direction occurs due to the effect of camber angle.