3D Motion of Rigid Bodies: A Foundation for Robot Dynamics AnalysisSpringer, 2018 M12 6 - 474 páginas This book offers an excellent complementary text for an advanced course on the modelling and dynamic analysis of multi-body mechanical systems, and provides readers an in-depth understanding of the modelling and control of robots. While the Lagrangian formulation is well suited to multi-body systems, its physical meaning becomes paradoxically complicated for single rigid bodies. Yet the most advanced numerical methods rely on the physics of these single rigid bodies, whose dynamic is then given among multiple formulations by the set of the Newton–Euler equations in any of their multiple expression forms. This book presents a range of simple tools to express in succinct form the dynamic equation for the motion of a single rigid body, either free motion (6-dimension), such as that of any free space navigation robot or constrained motion (less than 6-dimension), such as that of ground or surface vehicles. In the process, the book also explains the equivalences of (and differences between) the different formulations. |
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Página ix
... .. 16 1.1.3 Basic Matrix Operations.......................... 17 1.1.4 Square Matrices ................................ 31 1.1.5 Square Block Matrices ........................... 38 1.2 Linear Operators.............................
... .. 16 1.1.3 Basic Matrix Operations.......................... 17 1.1.4 Square Matrices ................................ 31 1.1.5 Square Block Matrices ........................... 38 1.2 Linear Operators.............................
Página xvi
... matrix Symmetric part of matrix A Skew-symmetric part of matrix A Input driving matrix (1) Coriolis matrix in quasi-Lagrangian coordinates (2) Input restrictive ... matrix of order 6 whose block components xvi Nomenclature Matrices.
... matrix Symmetric part of matrix A Skew-symmetric part of matrix A Input driving matrix (1) Coriolis matrix in quasi-Lagrangian coordinates (2) Input restrictive ... matrix of order 6 whose block components xvi Nomenclature Matrices.
Página xvii
... matrix of order 6 whose block components are given by CPOs (2) Submatrix of proper dimensions (3) [Kinematic] Reduced motion operator T [Dynamic] Coordinates transformation/separation during restricted motion U Kinematic restriction ...
... matrix of order 6 whose block components are given by CPOs (2) Submatrix of proper dimensions (3) [Kinematic] Reduced motion operator T [Dynamic] Coordinates transformation/separation during restricted motion U Kinematic restriction ...
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A Foundation for Robot Dynamics Analysis Ernesto Olguín Díaz. 1.1 Matrices Definition 1.4 (Matrix) A Matrix “A” is a ... [block] matrices of proper dimensions All A12 . . . Alj . . . Ain A21 A22 . . . A2; . . . A2n A | . . : - A ...
A Foundation for Robot Dynamics Analysis Ernesto Olguín Díaz. 1.1 Matrices Definition 1.4 (Matrix) A Matrix “A” is a ... [block] matrices of proper dimensions All A12 . . . Alj . . . Ain A21 A22 . . . A2; . . . A2n A | . . : - A ...
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... Matrix) A matrix is said to be positive (nonnegative) if all and everyone of its elements are positive (nonnegative): ... block elements and horizontal block elements. This matrix is said to be upper triangular if each element Aij ...
... Matrix) A matrix is said to be positive (nonnegative) if all and everyone of its elements are positive (nonnegative): ... block elements and horizontal block elements. This matrix is said to be upper triangular if each element Aij ...
Contenido
| 1 | |
| 2 | |
| 3 | |
2 Classical Mechanics | 101 |
Part II Free Motion of Single Rigid Body | 145 |
3 Rigid Motion | 147 |
4 Attitude Representations | 184 |
5 Dynamics of a Rigid Body | 231 |
7 Lagrangian Formulation | 306 |
Part III Constraint Motion of a Single Rigid Body | 329 |
8 Model Reduction Under Motion Constraint | 331 |
A The Cross Product Operator | 370 |
B Fundamentals of Quaternion Theory | 385 |
C Extended Operators | 401 |
D Examples for the Center of Mass and Inertia Tensors of Basic Shapes | 411 |
6 Spacial Vectors Approach | 273 |
Otras ediciones - Ver todas
3D Motion of Rigid Bodies: A Foundation for Robot Dynamics Analysis Ernesto Olguín Díaz Sin vista previa disponible - 2019 |
Términos y frases comunes
3D vector algebra angular velocity arise Attitude Kinematic Operator attitude representation axis base frame basic rotations block matrix Cartesian center of mass column computed constraint contact forces Coriolis matrix cross product defined Definition derivative diagonal dimension dot product dy dz dynamic eigenvalues elements ellipsoid elliptical prism equation equivalent Euclidean Euler angles Example frame coordinates function given gravity identity inertia matrix inertia moments inertia tensor inertial frame integral inverse inverse kinematic kinetic energy Lagrangian last expression linear operator mass vector momentum motion non-inertial frame norm null space octant orthogonal parallelepiped particle position Property pseudo-inverse quaternion product reference frame Remark Notice rigid body rotation matrix ſ ſ scalar singular values ſº solution spacial vector square matrix symmetric term Theorem torque transformation twist unit quaternion wrench written yields