• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.356-359
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• 2007

In this paper, the stability of a rotating cantilever pipe conveying fluid with a crack is investigated by the numerical method. That is, the influences of the rotating angular velocity, mass ratio and crack severity on the critical flow velocity for flutter instability of system are studied. The equations of motion of rotating pipe are derived using the Euler beam theory and the Lagrange's equation. The crack section of pipe is represented by a local flexibility matrix connecting two undamaged pipe segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. Generally, the critical flow velocity for flutter is proportional to the angular velocity and the depth of crack. Also, the critical flow velocity and stability maps of the rotating pipe system as a function of mass ratio for the changing each parameter are obtained.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.2
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• pp.94-101
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• 1996

The equations of motion for a basic industrial robotic system which has a rigid or a flexible arm are derived by Lagrange's equation, respectively. Especially, for the deflection of the flexible arm, the assumed mode method is employed. These equations are highly nonlinear equations with nonlinear coupling between the variables of motion. In order to design the control law for the rigid-arm robot, Hunt-Su's nonlinear transformation method and Marino's feedback equivalence condition are used with linear quadratic regulator(LQR) theory. The control law for the rigid-arm robot is employed to input the desired path and to provide the required nonlinear transformations for the flexible-arm robot to follow. By using the implicit Euler method to solve the nonlinear equations, the comparison of the motions between the flexible and the rigid robots and the effect of flexibility are examined.

• Computers and Concrete
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• v.32 no.6
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• pp.543-551
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• 2023

In this article, thermal post-buckling and primary resonance of the porous functionally graded material (FGM) beams in thermal environment considering the geometric imperfection are studied, the material properties of FGM beams are assumed to vary along the thickness of the beam, meanwhile, the porosity volume fraction, geometric imperfection, temperature, and the elastic foundation are considered, using the Euler-Lagrange equation, the nonlinear vibration equations are derived, after the dimensionless processing, the dimensionless equations of motion can be obtained. Then, the two-step perturbation method is applied to solve the vibration problems, the resonance and thermal post-buckling response relations are obtained. Finally, the functionally graded index, the porosity volume fraction, temperature, geometric imperfection, and the elastic foundation on the resonance behaviors of the FGM beams are presented. It can be found that these parameters can influence the thermal post-buckling and primary resonance problems.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.343-343
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• 2000

The conventional actuators with the speed reducer had weakness in supporting the weight of the body and leg itself. To overcome this, a new four bar link mechanism actuated by the ball screw was proposed. Using this, we developed a new type of 10 D.O.F biped robot. The dynamics model of the biped robot is investigated in this paper. In the modeling process, the robot dynamics are expressed in the joint coordinates using the Euler-Lagrange equation. Then, they are converted in to the sliding joint coordinates, and joint torques are expressed in the force along the sliding direction of the ball screw. To test modeling of the robot, a computer simulation was performed.

• Structural Engineering and Mechanics
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• v.40 no.4
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• pp.583-594
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• 2011

In the present study, free vibration of an axially functionally graded (AFG) pile embedded in Winkler-Pasternak elastic foundation is analyzed within the framework of the Euler-Bernoulli beam theory. The material properties of the pile vary continuously in the axial direction according to the power-law form. The frequency equation is obtained by using Lagrange's equations. The unknown functions denoting the transverse deflections of the AFG pile is expressed in modal form. In this study, the effects of material variations, the parameters of the elastic foundation on the fundamental frequencies are examined. It is believed that the tabulated results will be a reference with which other researchers can compare their results.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.534-537
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• 2004

In this paper, a dynamic behavior of spring supported cantilever beam with a crack and a moving mass is presented. Based on the Euler-Bernoulli beam theory, the equation of motion can be constructed by using the Lagrange's eauation. 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. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. And the crack is assumed to be in the first mode of fracture. As the depth of the crack is increased the tip displacement of the cantilever beam is increased.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.303-308
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• 1995

We consider a torus T, that is, a compact surface with genus 1 and $\Omega = D^2 \times S^1$ topologically with $\partial\Omega = T$, where $D^2$ is the open unit disk and $S^1$ is the unit circle. Let $\omega = (x,y)$ denote the generic point on T. For a smooth immersion $u : T \to R^3$, we define the Dirichlet functional by $$ E(u) = \frac{2}{1} \int_{T} $\mid$\nabla u$\mid$^2 d\omega $$ and the volume functional by $$ V(u) = \frac{3}{1} \int_{T} u \cdot u_x \Lambda u_y d\omege $$.

• 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.