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10 results on '"Lagrangian equations of motion"'

1. Nonlinear nonholonomic systems: a simple approach and various examples.

Author

Talamucci, Federico

Abstract

The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematical type (anolonomic constraints). The setting up of the equations of motion follows a simple principle which generalizes the holonomic case. Furthermore, attention is paid to the fact that the kinematical variables retain their velocity meaning, without resorting to the pseudo-velocity technique. Particular situations are examined in which the modeling of the constraints can be carried out in several ways to evaluate their effective equivalence. Numerous examples, many of which taken from the most recurring ones in the literature, are provided in order to illustrate the proposed theory. [ABSTRACT FROM AUTHOR]

Published
2024
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2. Rheonomic Systems with Nonlinear Nonholonomic Constraints: The Voronec Equations.

Author

Talamucci, Federico

Abstract

One of the earliest formulations of dynamics of nonholonomic systems traces back to 1895 and is due to Chaplygin, who developed his analysis under the assumption that a certain number of the generalized coordinates do not occur either in the kinematic constraints or in the Lagrange function. A few years later Voronec derived equations of motion for nonholonomic systems removing the restrictions demanded by the Chaplygin systems. Although the methods encountered in the following years favor the use of the quasi-coordinates, we will pursue the Voronec method, which deals with the generalized coordinates directly. The aim is to establish a procedure for extending the equations of motion to nonlinear nonholonomic systems, even in the rheonomic case. [ABSTRACT FROM AUTHOR]

Published
2020
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3. Equations of Motion of Free-Floating Spacecraft-Manipulator Systems: An Engineer's Tutorial

Author

Markus Wilde, Stephen Kwok Choon, Alessio Grompone, and Marcello Romano

Subjects
robot dynamics modeling, spacecraft manipulator dynamics, generalized Jacobian, generalized inertia matrix, Lagrangian equations of motion, Mechanical engineering and machinery, TJ1-1570, Electronic computers. Computer science, QA75.5-76.95
Abstract

The paper provides a step-by-step tutorial on the Generalized Jacobian Matrix (GJM) approach for modeling and simulation of spacecraft-manipulator systems. The General Jacobian Matrix approach describes the motion of the end-effector of an underactuated manipulator system solely by the manipulator joint rotations, with the attitude and position of the base-spacecraft resulting from the manipulator motion. The coupling of the manipulator motion with the base-spacecraft are thus expressed in a generalized inertia matrix and a GJM. The focus of the paper lies on the complete analytic derivation of the generalized equations of motion of a free-floating spacecraft-manipulator system. This includes symbolic analytic expressions for all inertia property matrices of the system, including their time derivatives and joint-angle derivatives, as well as an expression for the generalized Jacobian of a generic point on any link of the spacecraft-manipulator system. The kinematics structure of the spacecraft-manipulator system is described both in terms of direction-cosine matrices and unit quaternions. An additional important contribution of this paper is to propose a new and more detailed definition for the modes of maneuvering of a spacecraft-manipulator. In particular, the two commonly used categories free-flying and free-floating are expanded by the introduction of five categories, namely floating, rotation-floating, rotation-flying, translation-flying, and flying. A fully-symbolic and a partially-symbolic option for the implementation of a numerical simulation model based on the proposed analytic approach are introduced and exemplary simulation results for a planar four-link spacecraft-manipulator system and a spatial six-link spacecraft manipulator system are presented.

Published
2018
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4. Equations of Motion of Free-Floating Spacecraft-Manipulator Systems: An Engineer's Tutorial

Author

Stephen Kwok Choon, Alessio Grompone, Marcello Romano, Markus Wilde, Spacecraft Robotics Laboratory, and Naval Postgraduate School (U.S.)

Subjects
0209 industrial biotechnology, Generalized Jacobian, Computer science, lcsh:Mechanical engineering and machinery, media_common.quotation_subject, ComputerApplications_COMPUTERSINOTHERSYSTEMS, 02 engineering and technology, Kinematics, Inertia, Lagrangian equations of motion, lcsh:QA75.5-76.95, Computer Science::Robotics, 03 medical and health sciences, symbols.namesake, Sylvester's law of inertia, Matrix (mathematics), 020901 industrial engineering & automation, 0302 clinical medicine, generalized Jacobian, Artificial Intelligence, Control theory, generalized inertia matrix, Methods, lcsh:TJ1-1570, Quaternion, media_common, Robotics and AI, Equations of motion, Computer Science Applications, spacecraft manipulator dynamics, Jacobian matrix and determinant, Physics::Space Physics, symbols, lcsh:Electronic computers. Computer science, robot dynamics modeling, 030217 neurology & neurosurgery
Abstract

The article of record as published may be found at http://dx.doi.org/10.3389/frobt.2018.00041 The paper provides a step-by-step tutorial on the Generalized Jacobian Matrix (GJM) approach for modeling and simulation of spacecraft-manipulator systems. The General Jacobian Matrix approach describes the motion of the end-effector of an underactuated manipulator system solely by the manipulator joint rotations, with the attitude and position of the base-spacecraft resulting from the manipulator motion. The coupling of the manipulator motion with the base-spacecraft are thus expressed in a generalized inertia matrix and a GJM. The focus of the paper lies on the complete analytic derivation of the generalized equations of motion of a free-floating spacecraft-manipulator system. This includes symbolic analytic expressions for all inertia property matrices of the system, including their time derivatives and joint-angle derivatives, as well as an expression for the generalized Jacobian of a generic point on any link of the spacecraft-manipulator system. The kinematics structure of the spacecraft-manipulator system is described both in terms of direction-cosine matrices and unit quaternions. An additional important contribution of this paper is to propose a new and more detailed definition for the modes of maneuvering of a spacecraft-manipulator. In particular, the two commonly used categories free-flying and free-floating are expanded by the introduction of five categories, namely floating, rotation-floating, rotation-flying, translation-flying, and flying. A fully-symbolic and a partially-symbolic option for the implementation of a numerical simulation model based on the proposed analytic approach are introduced and exemplary simulation results for a planar four-link spacecraft-manipulator system and a spatial six-link spacecraft manipulator system are presented.

Published
2018

6. Geometrické řízení hadům podobných robotů

Author

Vašík, Petr, Návrat, Aleš, Shehadeh, Mhd Ali, Vašík, Petr, Návrat, Aleš, and Shehadeh, Mhd Ali

Abstract

This master’s thesis describes equations of motion for dynamic model of nonholonomic constrained system, namely the trident robotic snakes. The model is studied in the form of Lagrange's equations and D’Alembert’s principle is applied. Actually this thesis is a continuation of the study going at VUT about the simulations of non-holonomic mechanisms, specifically robotic snakes. The kinematics model was well-examined in the work of of Byrtus, Roman and Vechetová, Jana. So here we provide equations of motion and address the motion planning problem regarding dynamics of the trident snake equipped with active joints through basic examples and propose a feedback linearization algorithm., This master’s thesis describes equations of motion for dynamic model of nonholonomic constrained system, namely the trident robotic snakes. The model is studied in the form of Lagrange's equations and D’Alembert’s principle is applied. Actually this thesis is a continuation of the study going at VUT about the simulations of non-holonomic mechanisms, specifically robotic snakes. The kinematics model was well-examined in the work of of Byrtus, Roman and Vechetová, Jana. So here we provide equations of motion and address the motion planning problem regarding dynamics of the trident snake equipped with active joints through basic examples and propose a feedback linearization algorithm.

7. Geometrické řízení hadům podobných robotů

Author

Vašík, Petr, Návrat, Aleš, Vašík, Petr, and Návrat, Aleš

Abstract

This master’s thesis describes equations of motion for dynamic model of nonholonomic constrained system, namely the trident robotic snakes. The model is studied in the form of Lagrange's equations and D’Alembert’s principle is applied. Actually this thesis is a continuation of the study going at VUT about the simulations of non-holonomic mechanisms, specifically robotic snakes. The kinematics model was well-examined in the work of of Byrtus, Roman and Vechetová, Jana. So here we provide equations of motion and address the motion planning problem regarding dynamics of the trident snake equipped with active joints through basic examples and propose a feedback linearization algorithm., This master’s thesis describes equations of motion for dynamic model of nonholonomic constrained system, namely the trident robotic snakes. The model is studied in the form of Lagrange's equations and D’Alembert’s principle is applied. Actually this thesis is a continuation of the study going at VUT about the simulations of non-holonomic mechanisms, specifically robotic snakes. The kinematics model was well-examined in the work of of Byrtus, Roman and Vechetová, Jana. So here we provide equations of motion and address the motion planning problem regarding dynamics of the trident snake equipped with active joints through basic examples and propose a feedback linearization algorithm.

8. Geometrické řízení hadům podobných robotů

Author

Vašík, Petr, Návrat, Aleš, Vašík, Petr, and Návrat, Aleš

Abstract

This master’s thesis describes equations of motion for dynamic model of nonholonomic constrained system, namely the trident robotic snakes. The model is studied in the form of Lagrange's equations and D’Alembert’s principle is applied. Actually this thesis is a continuation of the study going at VUT about the simulations of non-holonomic mechanisms, specifically robotic snakes. The kinematics model was well-examined in the work of of Byrtus, Roman and Vechetová, Jana. So here we provide equations of motion and address the motion planning problem regarding dynamics of the trident snake equipped with active joints through basic examples and propose a feedback linearization algorithm., This master’s thesis describes equations of motion for dynamic model of nonholonomic constrained system, namely the trident robotic snakes. The model is studied in the form of Lagrange's equations and D’Alembert’s principle is applied. Actually this thesis is a continuation of the study going at VUT about the simulations of non-holonomic mechanisms, specifically robotic snakes. The kinematics model was well-examined in the work of of Byrtus, Roman and Vechetová, Jana. So here we provide equations of motion and address the motion planning problem regarding dynamics of the trident snake equipped with active joints through basic examples and propose a feedback linearization algorithm.

9. Geometrické řízení hadům podobných robotů

Author

Vašík, Petr, Návrat, Aleš, Vašík, Petr, and Návrat, Aleš

Abstract

This master’s thesis describes equations of motion for dynamic model of nonholonomic constrained system, namely the trident robotic snakes. The model is studied in the form of Lagrange's equations and D’Alembert’s principle is applied. Actually this thesis is a continuation of the study going at VUT about the simulations of non-holonomic mechanisms, specifically robotic snakes. The kinematics model was well-examined in the work of of Byrtus, Roman and Vechetová, Jana. So here we provide equations of motion and address the motion planning problem regarding dynamics of the trident snake equipped with active joints through basic examples and propose a feedback linearization algorithm., This master’s thesis describes equations of motion for dynamic model of nonholonomic constrained system, namely the trident robotic snakes. The model is studied in the form of Lagrange's equations and D’Alembert’s principle is applied. Actually this thesis is a continuation of the study going at VUT about the simulations of non-holonomic mechanisms, specifically robotic snakes. The kinematics model was well-examined in the work of of Byrtus, Roman and Vechetová, Jana. So here we provide equations of motion and address the motion planning problem regarding dynamics of the trident snake equipped with active joints through basic examples and propose a feedback linearization algorithm.

10. Geometrické řízení hadům podobných robotů

Author

Vašík, Petr, Návrat, Aleš, Shehadeh, Mhd Ali, Vašík, Petr, Návrat, Aleš, and Shehadeh, Mhd Ali

Abstract

This master’s thesis describes equations of motion for dynamic model of nonholonomic constrained system, namely the trident robotic snakes. The model is studied in the form of Lagrange's equations and D’Alembert’s principle is applied. Actually this thesis is a continuation of the study going at VUT about the simulations of non-holonomic mechanisms, specifically robotic snakes. The kinematics model was well-examined in the work of of Byrtus, Roman and Vechetová, Jana. So here we provide equations of motion and address the motion planning problem regarding dynamics of the trident snake equipped with active joints through basic examples and propose a feedback linearization algorithm., This master’s thesis describes equations of motion for dynamic model of nonholonomic constrained system, namely the trident robotic snakes. The model is studied in the form of Lagrange's equations and D’Alembert’s principle is applied. Actually this thesis is a continuation of the study going at VUT about the simulations of non-holonomic mechanisms, specifically robotic snakes. The kinematics model was well-examined in the work of of Byrtus, Roman and Vechetová, Jana. So here we provide equations of motion and address the motion planning problem regarding dynamics of the trident snake equipped with active joints through basic examples and propose a feedback linearization algorithm.

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