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. |
Dentro del libro
Página xiii
... Cartesian vectors , written with the three Cartesian coordinates of the Euclidean space ER Extended rotation ETO SE ( 3 ) Extended translation operator Special Euclidean group of order 3 SO ( 3 ) Special orthogonal group of order 3 SV ...
... Cartesian vectors , written with the three Cartesian coordinates of the Euclidean space ER Extended rotation ETO SE ( 3 ) Extended translation operator Special Euclidean group of order 3 SO ( 3 ) Special orthogonal group of order 3 SV ...
Página xv
... cartesian position of a point १ ( 1 ) Generalized coordinates vector ( 2 ) Quaternion r rc V X α ε 0 λ ( 1 ) 3D relative distance vector , in general in coordinates of a non - inertial frame ( 2 ) 3D columns of a rotation matrix 3D ...
... cartesian position of a point १ ( 1 ) Generalized coordinates vector ( 2 ) Quaternion r rc V X α ε 0 λ ( 1 ) 3D relative distance vector , in general in coordinates of a non - inertial frame ( 2 ) 3D columns of a rotation matrix 3D ...
Página xix
... Cartesian coordinates of an Euclidian space ............................................. 77 Fig. 1.3 Right hand rule definition for Cartesian 3D frames .......... 77 Fig. 1.4 Different coordinate systems for the same position of a ...
... Cartesian coordinates of an Euclidian space ............................................. 77 Fig. 1.3 Right hand rule definition for Cartesian 3D frames .......... 77 Fig. 1.4 Different coordinate systems for the same position of a ...
Página xxi
... Cartesian coordinates ................ 414 414 Fig. D.3 Ellipsoid with Cartesian coordinates ..................... 415 Fig. D.4 Parallelepiped with Cartesian coordinates limits at x 2 1⁄20,a , y 2 1⁄20,b , and z 2 1⁄20,c ..............
... Cartesian coordinates ................ 414 414 Fig. D.3 Ellipsoid with Cartesian coordinates ..................... 415 Fig. D.4 Parallelepiped with Cartesian coordinates limits at x 2 1⁄20,a , y 2 1⁄20,b , and z 2 1⁄20,c ..............
Página xxii
... Cartesian coordinates ..................... 431 Fig. D.17 Sphere as a particular case of an ellipsoid ................. 433 Fig. D.18 Spheroid with Cartesian coordinates ..................... 433 Fig. D.19 Parallelepiped of Example D.4...
... Cartesian coordinates ..................... 431 Fig. D.17 Sphere as a particular case of an ellipsoid ................. 433 Fig. D.18 Spheroid with Cartesian coordinates ..................... 433 Fig. D.19 Parallelepiped of Example D.4...
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