• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.11
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• pp.11-21
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• 1996

Robot manipulators constituing multi-robot system must exert the desired motion force on an object to preserve tghe fine motion of it. The forces exerte on an object by the end-effectors of multi-inducing force and the internal force. Here, motion-inducing force effects the motion of an object, but internal force as lies in the null space of an object coordinate can't effect it. The motion of an object can't track exactly the desired motion by the effect of an object, but internal force as lies in the null space of the effect of internal force component, therefore internal force component must be considered. In this paper, first, under assumption that we can estimate exactly the parameter of dynamics, we constitute paper, first, under assumption that we can estimate exactly the parameter of dynamics, we constitute the controller concerning internal force. And we obtain the internal force as projecting force sensor readings onto the space spanned by null basis set of jacobian matrix. Using the resolved acceleration control method and the fact that internal force lies in the null space of jacobian matrix, we construct the robust control law to preserve the robustness with respect to the uncertainty of mainpulator parameters.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.539-542
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• 1996

The forces exerted on an object by the end-effectors of multi-manipulators are decomposed into the motion-inducing force and the internal force. Motion-inducing force effects the motion of an object and internal force can't effect it. The motion of an object can't track exactly the desired motion because of internal force component, therefore internal force component must be considered. In this paper using the resolved acceleration control method and the fact that internal force lies in the null space of jacobian matrix, we construct independently the position, motion-inducing force and internal force controller. Secondly we construct the robust controller to preserve the robustness with respect to the uncertainty of manipulator parameters.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.559-564
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• 1993

Nonlinear equation of motion of the flexible manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. The resulting equations of motion have a structure which is useful to reduce the number of terms calculated, to check correctness, or to extend the model to high order. A manipulator with a flexible 4 bar link mechanism is a constrained system whose equations are sensitive to numerical integration error. This constrained system is solved using the null space matrix of the constraint Jacobian matrix. Singular value decomposition is a stable algorithm to find the null space matrix.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.2071-2093
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• 2015

In this paper, we investigate the similarity transformations in the Minkowski n-space. We study the geometric invariants of non-null curves under the similarity transformations. Besides, we extend the fundamental theorem for a non-null curve according to a similarity motion of ${\mathbb{E}}_1^n$. We determine the parametrizations of non-null self-similar curves in ${\mathbb{E}}_1^n$.

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.635-645
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• 2012

In this study, we investigate the curvature functions of ruled surface with lightlike ruling for a null curve with Cartan frame in Minkowski 3-space. Also, we give relations between the curvature functions of this ruled surface and curvature functions of central normal surface. Finally, we use the curvature theory of the ruled surface for determine differential properties of a robot end-effector motion.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.237-240
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• 1996

Internal Force based control of dual redundant manipulator is proposed. One is resolved acceleration type control in the decoupled joint space which includes null motion space and the other is in the impedance control fashion in which the desired impedances are decoupled in three subspace, internal motion controlled space, orthogonal to that space, and the null motion controlled space. The internal force is formulated with its basis set meaningful. The object dynamics is also briefly evolved beforehand.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.1
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• pp.170-176
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• 1998

In this paper, the column space and null space of the Jacobian matrix were obtained by using the pseudo-inverse method and projection matrix. The equations of motion of the system were replaced by independent acceleration components using the null space matrix. The proposed method has the following advantages. (1) It is simple to derive the null space. (2) The efficiency is improved by getting rid of constrained force terms. (3) Neither null space updating nor coordinate partitioning method is required. The suggested algorithm is applied to a three-dimensional vehicle model to show the efficiency.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.12 no.2
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• pp.71-78
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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 all relative coordinates, velocities, and accelerations. Since the variables are tightly coupled by the position, velocity, and acceleration level coordinates, 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 variables, 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 variables only in terms of the variations of the independent variables. Finally, the relationships between the variations of all variables 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 variables variations.

• 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.