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 xvi
... constant inertial matrix of a single rigid body [ Dynamic ] Null space projector [ Kinematic ] Null space projector Order 3 rotation matrix S (1) Skew-symmetric matrix of order 6 whose block components xvi Nomenclature Matrices.
... constant inertial matrix of a single rigid body [ Dynamic ] Null space projector [ Kinematic ] Null space projector Order 3 rotation matrix S (1) Skew-symmetric matrix of order 6 whose block components xvi Nomenclature Matrices.
Página xvii
A Foundation for Robot Dynamics Analysis Ernesto Olguín Díaz. S (1) Skew-symmetric matrix of order 6 whose block ... S Vector space Z Field of integer numbers R i Reference frame i List of Figures Fig. 1.1 Schematic projection of ...
A Foundation for Robot Dynamics Analysis Ernesto Olguín Díaz. S (1) Skew-symmetric matrix of order 6 whose block ... S Vector space Z Field of integer numbers R i Reference frame i List of Figures Fig. 1.1 Schematic projection of ...
Página 15
... S ( A ) are square matrices formed with only r chosen out of n columns ( or r out of m rows ) : [ ...... , ac , ...... ] if m < n : Sr ) ( A ) = ari if m > n ∀l = ( 1 , 2 , ... , q ) , and q = ( max ( n , m ) ) ( 1.12 ) A if m = n ...
... S ( A ) are square matrices formed with only r chosen out of n columns ( or r out of m rows ) : [ ...... , ac , ...... ] if m < n : Sr ) ( A ) = ari if m > n ∀l = ( 1 , 2 , ... , q ) , and q = ( max ( n , m ) ) ( 1.12 ) A if m = n ...
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... s ) , becomes AB = A [ b1 , b2 , ... , bp ] = [ Ab1 , Ab2 , ... , Abp ] ∈ [ Fm × s From which the canonical matrix product can be defined as follows . Definition 1.29 ( The matrix product ) Consider two arrays A ∈ Fm × n and B ...
... s ) , becomes AB = A [ b1 , b2 , ... , bp ] = [ Ab1 , Ab2 , ... , Abp ] ∈ [ Fm × s From which the canonical matrix product can be defined as follows . Definition 1.29 ( The matrix product ) Consider two arrays A ∈ Fm × n and B ...
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... s ) and R = max ( m , n , s ) being respectively the smallest and biggest dimensions m , n or s of matrices A and B. Remark The Binet - Cauchy formula ( 1.16d ) , Gantmacher ( 1977 ) , Khailath ( 1980 ) , establishes the determinant of ...
... s ) and R = max ( m , n , s ) being respectively the smallest and biggest dimensions m , n or s of matrices A and B. Remark The Binet - Cauchy formula ( 1.16d ) , Gantmacher ( 1977 ) , Khailath ( 1980 ) , establishes the determinant of ...
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
angular velocity arise base frame basic rotations block matrix Cartesian center of mass computed Consider constraint contact forces Coriolis matrix cross product defined Definition derivative diagonal dimension dot product dy dz dynamic eigenvalues elements ellipsoid elliptical prism equation equivalent Euclidian Euler angles Example frame coordinates given gravity identity inertia matrix inertia moments inertia tensor inertial frame integral inverse inverse kinematic Izzc kinetic energy Lagrangian last expression momentum motion non-inertial frame norm null space octant orthogonal parallelepiped parameters particle position Proof Property quaternion product reference frame Remark Notice restriction rigid body robot rotation matrix scalar singular values spacial vector square matrix symmetric term Theorem torque transformation twist unit quaternion wrench yields ευ θα θω Σ₁ ӘК ду дх ᎧᎾ