• 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.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.926-930
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• 1993

An efficient method of formulating the equations of motion of multibody systems is presented. The equations of motion for each body are formulated by using Newton-Eulerian approach in their generic form. And then a transformation matrix which relates the global coordinates and relative coordinates is introduced to rewrite the equations of motion in terms of relative coordinates. When appropriate set of kinematic constraints equations in terms of relative coordinates is provided, the resulting differential and algebraic equations are obtained in a suitable form for computer implementation. The system geometry or topology is effectively described by using the path matrix and reference body operator.

• Korean Journal of Applied Biomechanics
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• v.12 no.1
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• pp.125-133
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• 2002

The purpose of this study was to develop a method for estimating 3-D coordinates of lower trunk muscles using orientation angles during a motion. Traditional 3-D motion analysis system with DLT technique was used to track down the locations of eight reference markers which were attached on the back of the subject. In order to estimate the orientations of individual lumbar vertebrae and musculoskeletal parameters of the lower trunk muscle, the rotation matrix of the middle trunk reference frame relative to the lower trunk reference frame was determined and the angular locations of individual lumbar vertebrae were estimated by partitioning the orientation angles (Cardan angles) that represent the relative angles between the rotations of the middle and lower trunks. When the orientation angles of individual intervertebral joints were known at a given instant, the instantaneous coordinates of the origin and insertion for all selected muscles relative to the L5 local reference frame were obtained by applying the transformation matrix to the original coordinates which were relative to a local reference frame (S1, L4, L3, L2, or L1) in a rotation sequence about the Z-, X- and Y-axes. The multiplication of transformation matrices was performed to estimate the geometry and kinematics of all selected muscles. The time histories of the 3-D coordinates of the origin and insertion of all selected muscles relative to the center of the L4-L5 motion segment were determined for each trial.

• Journal of Advanced Marine Engineering and Technology
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• v.38 no.5
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• pp.566-572
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• 2014

Recently, indoor navigation has been applied in large convention centers by using wireless sensor networks (WSNs), which provide not only a user's path to be traveled but also orientation and shopping information to increase user's convenience. This paper presents the localization system for estimating relative coordinates without pre-deployment of the reference node based on ultra wide band (UWB) ranging system, which is relatively suitable for indoor localization compared to other wireless communications, and azimuth sensor. The proposed localization system which consists of an azimuth sensor and a mobile node composed of three nodes estimates relative coordinates of the reference node without applying any recursive and time consumption algorithms. Also, in the process of estimating relative coordinates of the reference node, ranging errors are minimized through the proposed technique and the number of nodes can be reduced. Experimental results show the feasibility and validity of the proposed system.

• 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.

• 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.

• 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.27 no.8
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• pp.1303-1308
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• 2003

This research proposes an implementation method of linearized equations of motion for multibody systems with closed loops. The null space of the constraint Jacobian is first pre-multiplied to the equations of motion to eliminate the Lagrange multiplier and the equations of motion are reduced down to a minimum set of ordinary differential equations. The resulting differential equations are functions of ail relative coordinates, velocities, and accelerations. Since the coordinates, velocities, and accelerations are tightly coupled by the position, velocity, and acceleration level constraints, direct substitution of the relationships among these variables yields very complicated equations to be implemented. As a consequence, the reduced equations of motion are perturbed with respect to the variations of all coordinates, velocities, and accelerations, which are coupled by the constraints. The position, velocity and acceleration level constraints are also perturbed to obtain the relationships between the variations of all relative coordinates, velocities, and accelerations and variations of the independent ones. The perturbed constraint equations are then simultaneously solved for variations of all coordinates, velocities, and accelerations only in terms of the variations of the independent coordinates, velocities, and accelerations. Finally, the relationships between the variations of all coordinates, velocities, accelerations and these of the independent ones are substituted into the variational equations of motion to obtain the linearized equations of motion only in terms of the independent coordinate, velocity, and acceleration variations.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.893-898
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• 2004

This research proposes an implementation method of linearized equations of motion for multibody systems with closed loops. The null space of the constraint Jacobian is first pre multiplied to the equations of motion to eliminate the Lagrange multiplier and the equations of motion are reduced down to a minimum set of ordinary differential equations. The resulting differential equations are functions of all relative coordinates, velocities, and accelerations. Since the coordinates, velocities, and accelerations are tightly coupled by the position, velocity, and acceleration level constraints, direct substitution of the relationships among these variables yields very complicated equations to be implemented. As a consequence, the reduced equations of motion are perturbed with respect to the variations of all coordinates, velocities, and accelerations, which are coupled by the constraints. The position, velocity and acceleration level constraints are also perturbed to obtain the relationships between the variations of all relative coordinates, velocities, and accelerations and variations of the independent ones. The perturbed constraint equations are then simultaneously solved for variations of all coordinates, velocities, and accelerations only in terms of the variations of the independent coordinates, velocities, and accelerations. Finally, the relationships between the variations of all coordinates, velocities, accelerations and these of the independent ones are substituted into the variational equations of motion to obtain the linearized equations of motion only in terms of the independent coordinate, velocity, and acceleration variations.