• Journal of KSNVE
• /
• v.9 no.2
• /
• pp.363-370
• /
• 1999

In this study, we establish a theory for dynamic behaviors of an automatic ball balancer, analyze its dynamic characteristics, and provide its design guide line. Equations of motion are derived by using the polar coordinate system instead of the rectangular coordinate system which was previously used in other researches. After nondimensionalization of the equations, the perturbation method is applied to locate the equilibrium positions and to obtain the linearized equations of motion around the equilibrium positions. The Eigenvalue problem is used to verify the dynamic stability around the equilibrium positions. On the other hand, the time responses are computed from the nonlinear equations of motion by using a time integration method.

• Proceedings of the KSME Conference
• /
• 2000.04a
• /
• pp.548-555
• /
• 2000

The dynamic walking and the inverse dynamics of the biped walking robot is investigated in this paper. The biped robot is modeled with 14 degrees of freedom rigid bodies considering the walking pattern and kinematic construction of humanoid. The method of the computer aided multibody dynamics is applied to the dynamic analysis. The equations of motion of biped are initially represented as terms of the Cartesian coordinates, then they are converted to the minimum number of equations of motion in terms of the joint coordinates using the velocity transformation matrix. For the consideration of the relationships between the ground and foot, the holonomic constraints are added or deleted on the equations of motion. The number of these constraints can be changed by types of walking pattern with three modes. In order for the dynamic walking to be stabilizable, optimized trunk positions are iteratively determined by satisfying the system ZMP(Zero Moment Point) and ground conditions.

• Journal of the Korean Society for Precision Engineering
• /
• v.17 no.9
• /
• pp.133-144
• /
• 2000

The dynamic walking planning and the inverse dynamics of the biped robot is investigated in this paper. The biped robot is modeled with 14 degrees of freedom rigid bodies considering the walking pattern and kinematic construction of humanoid. The method of the computer aided multibody dynamics is applied to the dynamic analysis. The equations of motion of biped are initially represented as terms of the Cartesian corrdinates then they are converted to the minimum number of equations of motion in terms of the joint coordinates using the velocity transformation matrix. For the consideration of the relationships between the ground and foot the holonomic constraints are added or deleted on the equations of motion. the number of these constraints can be changed by types of walking patterns with three modes. In order for the dynamic walking to be stabilizable optimized trunk positions are iteratively determined by satisfying the system ZMP(Zero Moment Point) and ground conditions.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.20 no.10
• /
• pp.915-922
• /
• 2010

This paper presents an efficient method for determining the forced response of a spinning flexible disk-spindle system supported by fluid dynamic bearings(FDBs) in a computer hard disk drive(HDD). The spinning flexible disk-spindle system is represented by the asymmetric finite element equations of motion originating from the asymmetric dynamic coefficients of the FDBs and the gyroscopic moment of a spinning disk-spindle system. The proposed method utilizes only the right eigenvectors of the eigenvalue problem to transform the large asymmetric finite element equations of motion into a small number of coupled equations, guaranteeing the accuracy of their numerical integration. The results are then back-substituted into the equations of motion to determine the forced response. The effectiveness of the proposed method was verified by comparing it with the responses from the classical methods of mode superposition with the general eigenvalue problems, and mode superposition with modal approximation. The proposed method was shown to be effective in determining the forced response represented by the asymmetric finite element equations of motion of a spinning flexible disk-spindle system supported by FDBs.

• Journal of Mechanical Science and Technology
• /
• v.18 no.2
• /
• pp.193-202
• /
• 2004

This paper presents a computer method for the dynamic analysis of a system of rigid bodies in plane motion. The formulation rests upon the idea of replacing a rigid body by a dynamically equivalent constrained system of particles. Newton's second law is applied to study the motion of the resulting system of particles without introducing any rotational coordinates. A velocity transformation is used to transform the equations of motion to a reduced set. For an open-chain, this process automatically eliminates all of the non-working constraint forces and leads to an efficient integration of the equations of motion. For a closed-chain, suitable joints should be cut and few cut-joints constraint equations should be included. An example of a closed-chain is used to demonstrate the generality and efficiency of the proposed method.

• Journal of KSNVE
• /
• v.6 no.4
• /
• pp.469-474
• /
• 1996

Dynamic stability of an axially oscillating cantilever beam is investigated in this paper. The equations of motion are derived and transformed into non-dimensional ones. The equations include harmonically oscillating parameters which originate from the motion-induced stiffness variation. Using the equations, the multiple scale perturbation method is employed to obtain a stability diagram. The stability diagram shows that relatively large unstable regions exist around the frequencies of the first bending natural frequency, twice the first bending natural frequency, and twice the second bending natural frequency. The validity of the diagram is proved by direct numerical simulations of the dynamic system.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.14 no.12
• /
• pp.1354-1359
• /
• 2004

This paper is concerned with the application of perturbation method to the dynamic analysis of floating flexible body. In dealing with the dynamics of free-floating body, the rigid-body motions and elastic vibrations are analyzed separately. However, the rigid-body motions cause vibrations and elastic vibrations also affect rigid-body motions in turn, which indicates that the rigid-body motions and elastic vibrations are coupled in nature. The resulting equations of motion are hybrid and nonlinear. We can discretize the equations of motion by means of admissible functions but still we have to cope with nonlinear equations. In the previous paper, we proposed the use of perturbation method to the coupled equations of motion and derived zero-order and first-order equations of motion. The derivation process was lengthy and tedious. Hence, in this paper, we propose a new approach to the same problem by applying the perturbation method to the Lagrange's equations, thus providing a systematic approach to the addressed problem. Theoretical derivations show the efficacy of the proposed method.

• International Journal of Aeronautical and Space Sciences
• /
• v.2 no.1
• /
• pp.28-43
• /
• 2001

Developed in these two series of paper is a complex dynamic model representing the motion of aircraft on the ground and a computer program for numerical simulation. The first part of paper presents the theoretical derivation of equations of motion of the landing gear system based on the physical principle. Developed model is 'structured' in the sense that the undercarriage system is regarded as an assembly of strut, tire, and wheel, where each component is modeled by a separate module. These modules are linked with two external modules-the aircraft and the runway characteristics-to carry out dynamic analysis and numerical simulation of the aircraft motion on the ground. Three sets of coordinate system associated with strut, wheel/tire and runway are defined, and external loads to each component and response characteristics are examined. Lagrangian formulation is used to derive the undercarriage equations of motion relative to the moving aircraft, and the resultant forces and moments from the undercarriage are transformed to aircraft body axes.

• International Journal of Aeronautical and Space Sciences
• /
• v.2 no.2
• /
• pp.82-94
• /
• 2001

The purpose of this paper is to analyze the static and dynamic stability-of the unmanned airship under development ; the target airship's over-all length of hull is 50m and the maximum diameter is 12.5m. For the analysis, the dynamic model of an airship was defined and both the nonlinear and linear dynamic equations of motion were derived. Two different configuration models (KA002Y and KA003Y) of the airship were used for the target model of the static stability analysis and the dynamic stability analysis. From the result of analyses, though the airship is unstable in static stability, dynamic characteristics of the airship can provide the stable dynamic stability. All of the results, airship models and dynamic flight equations will be an important basement and basic information for the next step of developing the automatic flight control system(AFCS) and the stability augmentation system(SAS) for the unmanned airship as well as for the stratospheric airship in the future.

• Journal of Mechanical Science and Technology
• /
• v.18 no.7
• /
• pp.1086-1093
• /
• 2004

The modal characteristics of constrained multibody systems undergoing constant accelerated motions are investigated in this paper. Relative coordinates are employed to derive the equations of motion, which are generally nonlinear in terms of the coordinates. The dynamic equilibrium position of a constrained multibody system needs to be obtained from the nonlinear equations of motion, which are then linearized at the dynamic equilibrium position. The mass and the stiffness matrices for the modal analysis can be obtained from the linearized equations of motion. To verify the effectiveness and the accuracy of the proposed method, two numerical examples are solved and the results obtained by using the proposed method are compared with those obtained by analytical and other numerical methods. The proposed method is found to be accurate as well as effective in predicting the modal characteristics of constrained multibody systems undergoing constant accelerated motions.