• Proceedings of the KSME Conference
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• 2004.04a
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• pp.899-904
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• 2004

Multibody dynamics formulation has been developed based on relative cartesian coordinates for subsystem analysis. Relative cartesian coordinates are defined with respect to a reference body of a subsystem. Relative cartesian formulation inherits the same merits of absolute cartesian formulation, such as generality and easy implementation. Two methods have been applied. One is Largrange Multiplier Elimination method and the other is independent coordinate method. A 1/4 car simulation has been carried out to verify the formulations. Since both methods provide identical results, it proves the validity of the formulation.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.1724-1729
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• 2003

Two different subsystem synthesis methods with independent generalized coordinates have been developed and compared. In each formulation, the subsystem equations of motion are generated in terms of independent generalized coordinates. The first formulation is based on the relative Cartesian coordinates with respect to moving subsystem base (virtual) body. The second formulation is based on the relative joint coordinates using recursive formulation. Computational efficiency of the formulations has been compared theoretically by the operational counting method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.8
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• pp.1974-1984
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• 1994

This paper presents a relative coordinate formulation for constrained mechanical systems. Relative coordinates are defined along degrees of freedom of a joint. Graph theoretic analyses are performed to identify topological paths in mechanical systems. Cut constraints are generated to handle closed loop systems. Equations of motion are derived in the Cartesian space and transformed to the joint space. Relative generalized coordinates are corrected to satisfy the cut constraints by a parametrizatiom method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.10
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• pp.2483-2490
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• 1993

This paper presents a systematic formulation for the kinematic and dynamic analysis of flexible multibody systems. The system equations of motion are derived in terms of relative and elastic coordinates using velocity transformation technique. The position transformation equations that relate the relative and elastic coordinates to the Cartesian coordinates for the two contiguous flexible bodies are derived. The velocity transformation matrix is derived systematically corresponding to the type of kinematic joints connecting the bodies and system path matrix. This matrix is employed to represent the equations of motion in relative coordinate space. Two examples are taken to test the method developed here.

• Journal of Mechanical Science and Technology
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• v.17 no.8
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• pp.1133-1139
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• 2003

In this paper, a numerical algorithm for the kinematic analysis of a multi-link five-point suspension system is presented. The kinematic analysis is carried out in terms of the rectangular Cartesian coordinates of some defined points in the links and at the joints. Geometric constraints are introduced to fix the relative positions between the points belonging to the same rigid body. Position, velocity and acceleration analyses are carried out. The presented formulation in terms or this system of coordinates is simple and involves only elementary mathematics. The results of the kinematic analysis are presented and discussed.

• Journal of Mechanical Science and Technology
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• v.19 no.spc1
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• pp.312-319
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• 2005

For real time dynamic simulation, two different subsystem synthesis methods with independent generalized coordinates have been developed and compared. In each formulation, the subsystem equations of motion are generated in terms of independent generalized coordinates. The first formulation is based on the relative Cartesian coordinates with respect to moving subsystem base body. The second formulation is based on the relative joint coordinates using recursive formulation. Computational efficiency of the formulations has been compared theoretically by the arithmetic operational counts. In order to verify real-time capability of the formulations, bump run simulations of a quarter car model with SLA suspension subsystem have been carried out to measure the actual CPU time.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.2
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• pp.352-360
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• 1997

An inverse dynamic procedure for spatial multibody systems containing flexible bodies is developed in the relative joint coordinate space. Constraint acceleration equations are derived in terms of relative coordinates using the velocity transformation technique. An inverse velocity transformation operator, which transforms the Cartesian velocities to the relative velocities, is derived systematically corresponding to the types of kinematic joints connecting the bodies and the system reference matrix. Using the resulting matrix, the joint reaction forces and moments are analyzed in the Cartesian coordinate space. The formulation is illustrated by means of two numerical examples.

• Journal of Mechanical Science and Technology
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• v.15 no.6
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• pp.693-698
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• 2001

The analysis of actuating forces (or torques) and joint reaction forces (or moments) are essential to determine the capacity of actuators, to control the system and to design the components. This paper presents an inverse dynamic analysis algorithm for flexible multibody systems with closed-loops in the relative joint coordinate space. The joint reaction forces are analyzed in Cartesian coordinate space using the inverse velocity transformation technique. The joint coordinates and the deformation modal coordinates are used as the generalized coordinates of a flexible multibody system. The algorithm is verified through the analysis of a slider-crank mechanism.

• 한국해양학회지
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• v.15 no.2
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• pp.112-122
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• 1980

A two-dimensional non-linear tidal model has been established to calculate the M$\_$2/ tide of Inchon Bay in the west coast of Korea. Cartesian coordinates are used for the derivation of the governing equations and account is taken of extensive drying boundaries (tidal flats) which are exposed at low tides. The tidal amplitudes and phases computed from the model agree well with those known from observation lying within bounds 5cm in amplitude and 5 in phase relative to the observed results. The work represents a further stage in the development including extensive sea measurements capable of application in various coastal engineering problems encountered in Inchon Bay area.

• Transactions of the Korean Society of Automotive Engineers
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• v.2 no.4
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• pp.80-90
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• 1994

Basic constraint equations derived from orthogonality conditions between a pair of body-fixed vectors and a body-fixed vector or a vector between two bodies are reformulated by using relative coordinate kinematics between two adjacent reference frames. Arithmetic numbers of operations required to compute derivatives of the constraint equations are drastically reduced. A mixed formulation of relative and cartesian coordinates is developed to further simplify derivatives of the constraints. Advantages and disadvantages of the new formulation are discussed. Possible singularity problem of para llelism constraints is resolved by introducing an extra generalized coordinate. Kinematic analysis of a McPherson strut suspension system are carried out to illustrate use and efficiency of the new formulation.