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

Description

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. Front Matter ....Pages i-xxiii Front Matter ....Pages 1-1 Mathematic Foundations (Ernesto Olguín Díaz)....Pages 3-100 Classical Mechanics (Ernesto Olguín Díaz)....Pages 101-144 Front Matter ....Pages 145-145 Rigid Motion (Ernesto Olguín Díaz)....Pages 147-183 Attitude Representations (Ernesto Olguín Díaz)....Pages 185-230 Dynamics of a Rigid Body (Ernesto Olguín Díaz)....Pages 231-271 Spacial Vectors Approach (Ernesto Olguín Díaz)....Pages 273-305 Lagrangian Formulation (Ernesto Olguín Díaz)....Pages 307-328 Front Matter ....Pages 329-329 Model Reduction Under Motion Constraint (Ernesto Olguín Díaz)....Pages 331-369 Back Matter ....Pages 371-474