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E-raamat: 3D Motion of Rigid Bodies: A Foundation for Robot Dynamics Analysis

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3D Motion of Rigid Bodies: A Foundation for Robot Dynamics AnalysisSuurem pilt
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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 NewtonEuler 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 (anddifferences between) the different formulations.

Arvustused

This book is a useful text for an advanced course on the dynamic modelling of multi-body mechanical systems, and provides readers a more clear understanding in the area of robots modeling and control. the intended audience consisting of mechanical and control researchers and engineers or graduate and PhD students in in the classical mechanics, robotics and mechatronics will find enough material that can be of some help in their independent studies. (Clementina Mladenova, zbMATH 1435.70001, 2020)

Part I Fundamentals
1 Mathematic Foundations
3(98)
1.1 Matrices
6(37)
1.1.1 The Determinant of a Matrix
10(6)
1.1.2 Other Basic Functions of a Matrix
16(1)
1.1.3 Basic Matrix Operations
17(14)
1.1.4 Square Matrices
31(7)
1.1.5 Square Block Matrices
38(5)
1.2 Linear Operators
43(34)
1.2.1 Vector Spaces
44(5)
1.2.2 Transformations
49(7)
1.2.3 Range Space and Null Space
56(5)
1.2.4 Eigenvalues and Eigenvectors
61(16)
1.3 3D Vector Analysis
77(24)
1.3.1 The Dot (Scalar) Product
80(3)
1.3.2 The Cross (Vector) Product
83(5)
1.3.3 Vectorial Geometry
88(3)
1.3.4 Vector Differentiation
91(10)
2 Classical Mechanics
101(46)
2.1 Newton's Mechanics of a Particle
101(11)
2.1.1 The Work and Energy
102(5)
2.1.2 The Power
107(3)
2.1.3 Final Comments
110(2)
2.2 Lagrange Mechanics for Multi-particle Systems
112(35)
2.2.1 D'Alembert-Lagrange's Equation
116(13)
2.2.2 The Euler-Lagrange's Equation
129(7)
2.2.3 Properties of Lagrangian Formulation
136(7)
2.2.4 Final Comments
143(4)
Part II Free Motion of Single Rigid Body
3 Rigid Motion
147(38)
3.1 Translations
147(2)
3.2 Rotations
149(16)
3.2.1 Attitude's Degrees of Freedom
153(1)
3.2.2 Basic Rotations
154(3)
3.2.3 Composed Rotations
157(3)
3.2.4 The Euler Theorem of Rotations
160(5)
3.3 The Rigid Motion Kinematics
165(20)
3.3.1 The Angular Velocity
166(13)
3.3.2 The Coriolis Effect
179(1)
3.3.3 The Linear Velocity and Acceleration
180(2)
3.3.4 Kinematic Equations
182(3)
4 Attitude Representations
185(46)
4.1 Pair of Rotation
186(6)
4.1.1 Computing the Axis/Angle Parameters from a Rotation Matrix
188(1)
4.1.2 The Angular Velocity for the Axis/Angle Representation
189(1)
4.1.3 Attitude Inverse Kinematics for the Axis/Angle Representation
190(2)
4.2 Roll-Pitch-Yaw Representation
192(6)
4.2.1 Computing the Roll, Pitch and Yaw Angles from a Rotation Matrix
193(2)
4.2.2 Angular Velocity and the Roll-Pitch-Yaw Representation
195(2)
4.2.3 Attitude Inverse Kinematics for the Roll-Pitch-Yaw Representation
197(1)
4.3 Euler Angles zyz
198(4)
4.3.1 Computing the zyz Euler Angles from a Rotation Matrix
199(1)
4.3.2 Angular Velocity and the zyz Representation
199(2)
4.3.3 Attitude Inverse Kinematics for the Euler Angles zyz Representation
201(1)
4.4 Unit Quaternions
202(17)
4.4.1 Equivalence with the Pair of Rotation
204(4)
4.4.2 Computing Quaternions from a Rotation Matrix
208(2)
4.4.3 Composed Rotation with Quaternions
210(2)
4.4.4 Angular Velocity with Quaternions
212(3)
4.4.5 Attitude Inverse Kinematics for the Quaternion Representation
215(4)
4.5 Rodrigues Parameters
219(11)
4.5.1 Computing Gibb's Vector from a Rotation Matrix
220(1)
4.5.2 Angular Velocity and Rodrigues Parameters
221(1)
4.5.3 Attitude Inverse Kinematics for Gibb's Representation
222(8)
4.6 Resume
230(1)
5 Dynamics of a Rigid Body
231(42)
5.1 The Center of Mass
234(5)
5.1.1 Kinematics at the Center of Mass
238(1)
5.2 The Kinetic Energy
239(8)
5.2.1 The Inertia Tensor
241(5)
5.2.2 Different Coordinates Expressions for the Kinetic Energy
246(1)
5.3 Momentums
247(3)
5.3.1 Linear Momentum Expression
247(1)
5.3.2 Angular Momentum Expression
248(2)
5.4 Rigid Dynamic Motion
250(8)
5.4.1 Euler's First Law of Motion
251(1)
5.4.2 Euler's Second Law of Motion
252(3)
5.4.3 The Newton-Euler Formulation
255(3)
5.5 Work and Power
258(2)
5.6 External Influences
260(3)
5.6.1 The Gravity Force
261(2)
5.7 Kirchhoff (Energy-Based) Formulation
263(10)
5.7.1 Kirchhoff-Euler Equivalence
264(2)
5.7.2 The Potential Energy
266(7)
6 Spacial Vectors Approach
273(34)
6.1 Spacial Vectors
273(3)
6.1.1 The Twist: the Velocity Spacial Vector
273(1)
6.1.2 The Wrench: the Force Spacial Vector
274(1)
6.1.3 The Pose
275(1)
6.1.4 The Motion and Force Spaces
276(1)
6.2 Spacial Vectors Transformations
276(7)
6.2.1 Extended Rotations
276(2)
6.2.2 Extended Translations
278(3)
6.2.3 The Spacial Vector Product
281(2)
6.3 Spacial Vector's Kinematics
283(5)
6.3.1 The Plucker Transformation
283(3)
6.3.2 The Pose Kinematics
286(2)
6.4 Spacial Vector's Dynamics
288(19)
6.4.1 The Power
288(1)
6.4.2 Kinetic Energy
288(2)
6.4.3 The Momentum's Spacial Vector
290(2)
6.4.4 Spacial Vector's Rigid Dynamic Motion
292(10)
6.4.5 Wrench of Exogenous Influences
302(5)
7 Lagrangian Formulation
307(24)
7.1 Direct Lagrangian Expression
308(7)
7.1.1 The Kinetic Energy and Inertia Matrix
308(2)
7.1.2 The Coriolis Matrix
310(2)
7.1.3 The Gravity Vector
312(2)
7.1.4 The Generalized Forces
314(1)
7.2 Indirect Lagrangian Formulation
315(11)
7.2.1 The quasi-Lagrangian Coordinates
315(1)
7.2.2 Indirect Lagrangian Equivalence
316(2)
7.2.3 Properties of Quasi-Lagrangian Formulation
318(8)
7.3 Conclusions
326(5)
Part III Constraint Motion of a Single Rigid Body
8 Model Reduction Under Motion Constraint
331(40)
8.1 The Constraint Model
332(2)
8.2 Model Reduction, the Dynamical Approach
334(17)
8.2.1 Example 1: The Omnidirectional Mobile Robot
335(11)
8.2.2 Example 2: The Differential Mobile Robot
346(5)
8.3 Twist Coordinates Separation: The Kinematical Approach for the Dynamic Model Reduction
351(18)
8.3.1 Wrench Coordinates Separation
354(1)
8.3.2 Kinematical Reduction of the Dynamic Model
355(4)
8.3.3 Example 3: The Omnidirectional Mobile Robot, Kinematic Approach
359(5)
8.3.4 Example 4: The Differential Mobile Robot, Kinematic Approach
364(5)
8.4 Resume
369(2)
Appendix A: The Cross Product Operator 371(14)
Appendix B: Fundamentals of Quaternion Theory 385(16)
Appendix C: Extended Operators 401(10)
Appendix D: Examples for the Center of Mass and Inertia
Tensors of Basic Shapes 411
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