• Korean Journal of Computational Design and Engineering
• /
• v.14 no.4
• /
• pp.261-270
• /
• 2009

We can save a lot of efforts and time to perform various kinds of multibody system dynamics simulations if the equations of motion of the multibody system can be formulated automatically. In general, the equations of motion are formulated based on Newton's $2^{nd}$law. And they can be transformed into the equations composed of independent variables by using velocity transformation matrix. In this paper the velocity transformation matrix is derived based on a topological modeling approach which considers the topology and the joint property of the multibody system. This approach is, then, used to formulate the equations of motion automatically and to implement a multibody system dynamics simulation program. To verify the the efficiency and convenience of the program, it is applied to the lifting simulation of a floating crane.

• Journal of Mechanical Science and Technology
• /
• v.14 no.2
• /
• pp.159-167
• /
• 2000

A computational method for the dynamic analysis of a constrained mechanical system is presented in this paper. The partial velocity matrix, which is the null space of the Jacobian of the constraint equations, is used as the key ingredient for the derivation of reduced equations of motion. The acceleration constraint equations are solved simultaneously with the equations of motion. Thus, the total number of equations to be integrated is equivalent to that of the pseudo generalized coordinates, which denote all the variables employed to describe the configuration of the system of concern. Two well-known conventional methods are briefly introduced and compared with the present method. Three numerical examples are solved to demonstrate the solution accuracy, the computational efficiency, and the numerical stability of the present method.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.33 no.12
• /
• pp.1433-1441
• /
• 2009

In multibody dynamic analysis, one of the most important problems is to reduce computation times for real-time simulation. This paper presents the derivation procedure of equations of motion of a 6${\times}$6 autonomous vehicle in terms of chassis local coordinates which do not require coordinates transformation matrix to enhance efficiency for real-time dynamic analysis. Also, equations of motion are derived using the VT(velocity transformation) technique and symbolic computation method coded by MATLAB. The Jacobian matrix of the equations of motion of a system is derived from symbolic operations to apply the implicit integration method. The analysis results were compared with ADAMS results to verify the accuracy and approve the feasibility of real time analysis.

• Proceedings of the KSME Conference
• /
• 2005.11a
• /
• pp.193.1-193.1
• /
• 2005

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.15 no.1
• /
• pp.366-375
• /
• 1991

In this study, vibrational behavior of uniform pipe carrying a moving medium is studied by using a transfer matrix and the displacement function derived from the conventional beam theory. In various boundary conditions, flow velocity and mechanical property change of the variation of natural frequency are investigated. The Coriolis term in the original differential equation of motion has been ignored in the investigation. This method is used to study the variation of natural frequency with flow velocity for clamped-clamped, cantilevered, clamped-pinned, pinned-pinned, free-free straight pipe element. It is shown that clamped-clamped, free-free pipe have the highest natural frequency and critical velocity values while cantilevered pipe have the smallest natural frequency for the same mechanical properties. From the vibration effects of mechanical property variation, it is shown that bending stiffness and pipe length variation has large influence on natural frequency and critical velocity. Since the order of transfer matrix is not changed with boundary conditions of pipe element, this method proposed can be easily applied to personal-computer for vibration analysis of pipe element. Furthermore, this method can be extended to three-dimensional system by using a coordinate transformation for the analysis of piping systems.

• Proceedings of the KSME Conference
• /
• 2000.11a
• /
• pp.576-583
• /
• 2000

A robust position control using a sliding mode controller is adopted for the stable dynamic walking of the biped. For the biped robot that is modeled with 14 degrees of freedom rigid bodies using the method of the multibody dynamics, the joint angles for simulation are obtained by the velocity transformation matrix using the given Cartesian foot and trunk trajectories. Hertz force model and Hysteresis damping element which is used in explanation of the energy dissipation during contact with ground are used for modeling of the ground reactions during the simulation. By the obtained that forces which contains highly confused noise elements and the system modeling uncertainties of various kinds such as unmodeled dynamics and parameter inaccuracies, the biped system will be unstable. For that problems, we are adopting a nonlinear robust control using a sliding mode controller. Under the assumption that the esimation error on the unknown parameters is bounded by a given function, that controller provides a successful way to preserve stability and achieve good performance, despite the presence of strong modeling imprecisions or uncertainties.

• Journal of the Korean Society for Precision Engineering
• /
• v.18 no.5
• /
• pp.137-146
• /
• 2001

A robust controller with the sliding mode is proposed for stable dynamic walking of the biped robot in this paper. For the robot system to be controlled, which is modeled as 14 DOF rigid bodies by the method of multi-body dynamics, the joint angle trajectories are determined by the velocity transformation matrix. Also Hertz force model and Hysteresis damping element are utilized for the ground reaction and impact forces during the contact with the ground. The biped robot system becomes unstable since those forces contain highly confused noise components and some discontinuity, and modeling uncertainties such as parameter inaccuracies. The sliding mode control is applied to solve above problems. Under the assumption of the bounded estimation errors on the unknown parameters, the proposed controller provides a successful way to achieve the stability and good performance in spite of the presence of modeling imprecisions of uncertainties.

• Smart Structures and Systems
• /
• v.32 no.1
• /
• pp.1-7
• /
• 2023

In modal analysis, the mode shape reflects the vibration characteristics of the structure, and thus it is widely performed for finite element model updating and structural health monitoring. Generally, the acceleration-based mode shape is suitable to express the characteristics of structures for the translational vibration; however, it is difficult to represent the rotational mode at boundary conditions. A tilt sensor and gyroscope capable of measuring rotational mode are used to analyze the overall behavior of the structure, but extracting its mode shape is the major challenge under the small vibration always. Herein, we conducted a feasibility study on a multi-mode shape estimating approach utilizing a single physical quantity signal. The basic concept of the proposed method is to receive multi-metric dynamic responses from two sensors and obtain mode shapes through bridge loading test with relatively large deformation. In addition, the linear transformation matrix for estimating two mode shapes is derived, and the mode shape based on the gyro sensor data is obtained by acceleration response using ambient vibration. Because the structure's behavior with respect to translational and rotational mode can be confirmed, the proposed method can obtain the total response of the structure considering boundary conditions. To verify the feasibility of the proposed method, we pre-measured dynamic data acquired from five accelerometers and five gyro sensors in a lab-scale test considering bridge structures, and obtained a linear transformation matrix for estimating the multi-mode shapes. In addition, the mode shapes for two physical quantities could be extracted by using only the acceleration data. Finally, the mode shapes estimated by the proposed method were compared with the mode shapes obtained from the two sensors. This study confirmed the applicability of the multi-mode shape estimation approach for accurate damage assessment using multi-dimensional mode shapes of bridge structures, and can be used to evaluate the behavior of structures under ambient vibration.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
• /
• v.1
• /
• pp.9-14
• /
• 2006

The authors aim to establish the theory necessary for developing the free gyrocompass. The following considerations are taken. One is to suggest north-finding principle by the angular velocity of the earth's rotation, and the other is to suggest that the motion rate of the spin axis in the free gyro frame is transformed into the platform fame and this transformed rate is again transformed into the NED navigation frame. After transformation ship's heading is obtained using the fore-aft and athwartship components of the motion rate of the spin axis in the NED frame In addition it was suggested how to solve the transformation matrix necessary for transforming each frame.

• International Journal of Precision Engineering and Manufacturing
• /
• v.2 no.1
• /
• pp.5-10
• /
• 2001

A method is proposed to obtain the Jacobian matrix of the 5 -bar parallel manipulator by employing the orthogonality between position and velocity vectors of rotating rigid-body around a fixed point. The dynamics of the 5-bar parallel manipulator is analyzed and utilized to design the computed-torque controller by developing a transformation matrix of the passive joints with respect to the active ones. In experimental demonstration, it shows that high-speed and accuracy tasks are performed by the proposed computed-torque control.