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
Resultados 6-10 de 90
Página 23
... Consider the case of an order 2 matrix given in Examples 1.14 , 1.16 , and 1.21 . Then the inverse of a 2 × 2 square matrix is given as 422-412 -a21 a11 A - 1 = a11a22 a12a21 Example 1.23 Consider the simple order 3 matrix whose ...
... Consider the case of an order 2 matrix given in Examples 1.14 , 1.16 , and 1.21 . Then the inverse of a 2 × 2 square matrix is given as 422-412 -a21 a11 A - 1 = a11a22 a12a21 Example 1.23 Consider the simple order 3 matrix whose ...
Página 24
... Consider the following matrix equations AX = B , YA B where A is square matrix such that | A | ≠ 0 and ( B , X , Y ) are rectangular matrices of the same dimensions . These equations have only one solution , respectively : X = A ̄1B ...
... Consider the following matrix equations AX = B , YA B where A is square matrix such that | A | ≠ 0 and ( B , X , Y ) are rectangular matrices of the same dimensions . These equations have only one solution , respectively : X = A ̄1B ...
Página 26
... Consider the scalar inner product of two col- umn matrices , i.e. a = ( x , y ) = x2 y = y7x = x1 y1 + x2 y2 + ··· + Xn yn . The par- T T tial derivatives with respect to x and y are , respectively 8 ( x , y ) дх = 8 ( x , y ) ду = д ...
... Consider the scalar inner product of two col- umn matrices , i.e. a = ( x , y ) = x2 y = y7x = x1 y1 + x2 y2 + ··· + Xn yn . The par- T T tial derivatives with respect to x and y are , respectively 8 ( x , y ) дх = 8 ( x , y ) ду = д ...
Página 27
... Consider the scalar inner product of two column matrices x = [ X1 , X2 , ... , xn ] and y = [ y1 , y2 , ... , ym ] , i.e. a = ( x , y ) = xT y = y x = x1 y1 + x2 y2 + ··· + Xn yn , and together with the condition that some elements of ...
... Consider the scalar inner product of two column matrices x = [ X1 , X2 , ... , xn ] and y = [ y1 , y2 , ... , ym ] , i.e. a = ( x , y ) = xT y = y x = x1 y1 + x2 y2 + ··· + Xn yn , and together with the condition that some elements of ...
Página 28
... Consider the ith element of the differentiation matrix above : д ( х , у ) д ( x1 y1 + x2 y2 + ··· + XnYn ) дхі = дхі = Σχ θα n дуј Vi + = Yi + ду дхі j = 1 Notice that de second term in the above expression can be written as дут T -x ...
... Consider the ith element of the differentiation matrix above : д ( х , у ) д ( x1 y1 + x2 y2 + ··· + XnYn ) дхі = дхі = Σχ θα n дуј Vi + = Yi + ду дхі j = 1 Notice that de second term in the above expression can be written as дут T -x ...
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