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 xiii
... written with the three Cartesian coordinates of the Euclidean space ER Extended rotation ETO Extended translation operator SEð3Þ Special Euclidean group of order 3 SOð3Þ Special orthogonal group of order 3 SV 6D spacial vector, made by ...
... written with the three Cartesian coordinates of the Euclidean space ER Extended rotation ETO Extended translation operator SEð3Þ Special Euclidean group of order 3 SOð3Þ Special orthogonal group of order 3 SV 6D spacial vector, made by ...
Página 20
... written as 〈a,b〉 = aTb Property 1.8 Since the inner product is a scalar, this product is commutative: Commutativity: 〈a,b〉 = aTb = bTa = 〈b,a〉 Remark Notice that it is sometimes used a different notation 20 1 Mathematic Foundations.
... written as 〈a,b〉 = aTb Property 1.8 Since the inner product is a scalar, this product is commutative: Commutativity: 〈a,b〉 = aTb = bTa = 〈b,a〉 Remark Notice that it is sometimes used a different notation 20 1 Mathematic Foundations.
Página 22
... written as 〈A, B〉 F Remark Notice that the Frobenius product within the same matrix A : A = tr(A∗T A) = tr(AA∗T) = |2 > 0 (1.18) |ai,j n∑ m∑ i=1 n∑ j=1 is the element-wise addition of the square modulus of all the elements of ...
... written as 〈A, B〉 F Remark Notice that the Frobenius product within the same matrix A : A = tr(A∗T A) = tr(AA∗T) = |2 > 0 (1.18) |ai,j n∑ m∑ i=1 n∑ j=1 is the element-wise addition of the square modulus of all the elements of ...
Página 28
... written as | y JC E JC; T y x. Then the full differential matrix yields (1.20). JC; Definition 1.45 (Differentiation of a Matrix Product) Given a product of matrices A and B of proper dimensions e F, the scalar differentiation is given ...
... written as | y JC E JC; T y x. Then the full differential matrix yields (1.20). JC; Definition 1.45 (Differentiation of a Matrix Product) Given a product of matrices A and B of proper dimensions e F, the scalar differentiation is given ...
Página 29
... written as the scalar inner products: B(x, y) = yT A x = 〈x,z〉=〈y,w〉 After Example 1.27, the gradients of the inner products above with respect to x and y are, respectively ∂B(x, ∂x y) = ∂ 〈x,z〉 ∂x = z = AT y, ∂B(x, ∂y y) ...
... written as the scalar inner products: B(x, y) = yT A x = 〈x,z〉=〈y,w〉 After Example 1.27, the gradients of the inner products above with respect to x and y are, respectively ∂B(x, ∂x y) = ∂ 〈x,z〉 ∂x = z = AT y, ∂B(x, ∂y y) ...
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