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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... .............. 157 3.2.4 The Euler Theorem of Rotations .................... 160 3.3 The Rigid Motion Kinematics ........................... 165 3.3.1 The Angular Velocity ........................... 166 3.3.2 The Coriolis Effect ...
... .............. 157 3.2.4 The Euler Theorem of Rotations .................... 160 3.3 The Rigid Motion Kinematics ........................... 165 3.3.1 The Angular Velocity ........................... 166 3.3.2 The Coriolis Effect ...
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... theorem applied to 3D vectors................ 79 Fig. 1.6 Canonical basis unit vectors, the unit sphere and the ... Theorem ...... 94 Fig. 1.16 Type I area D for Green's Theorem with boundaries given by 4 curves C1 , C2 , C3 , and ...
... theorem applied to 3D vectors................ 79 Fig. 1.6 Canonical basis unit vectors, the unit sphere and the ... Theorem ...... 94 Fig. 1.16 Type I area D for Green's Theorem with boundaries given by 4 curves C1 , C2 , C3 , and ...
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... Theorem 1.1 If the block matrices A and B in ( 1.44 ) are orthogonal complements fulfilling the following condition : AT B 0 Then the inverse of E = [ A B ] is given as E - 1 -1 E = [ A B ] = [ A + ] ] B + Fnxn where A + and B + are the ...
... Theorem 1.1 If the block matrices A and B in ( 1.44 ) are orthogonal complements fulfilling the following condition : AT B 0 Then the inverse of E = [ A B ] is given as E - 1 -1 E = [ A B ] = [ A + ] ] B + Fnxn where A + and B + are the ...
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... Theorem 1.2 ( Linearly independency condition Gantmacher 1977 ) In order that the vectors ( X1 , X2 , ... , Xm ) ∈ Fn be linearly independent it is necessary and sufficient condition that the rank of the matrix X formed with the ...
... Theorem 1.2 ( Linearly independency condition Gantmacher 1977 ) In order that the vectors ( X1 , X2 , ... , Xm ) ∈ Fn be linearly independent it is necessary and sufficient condition that the rank of the matrix X formed with the ...
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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