A Concise Introduction to Mechanics of Rigid Bodies: Multidisciplinary Engineering

ISBN-13: 9783319831947 / Angielski / Miękka / 2018 / 191 str.

L. Huang

Opis

With simplified mathematical equations that illuminate the theoretical foundations of robotics and mechanics, this volume provides comprehensive coverage of statics and dynamics together, giving readers a more balanced understanding of their relationship.

This updated second edition broadens the explanation of rotational kinematics and dynamics - the most important aspect of rigid body motion in three-dimensional space and a topic of much greater complexity than linear motion. It expands treatment of vector and matrix, and includes quaternion operations to describe and analyze rigid body motion which are found in robot control, trajectory planning, 3D vision system calibration, and hand-eye coordination of robots in assembly work, etc. It features updated treatments of concepts in all chapters and case studies. The textbook retains its comprehensiveness in coverage and compactness in size, which make it easily accessible to the readers from multidisciplinary areas who want to grasp the key concepts of rigid body mechanics which are usually scattered in multiple volumes of traditional textbooks. Theoretical concepts are explained through examples taken from across engineering disciplines and links to applications and more advanced courses (e.g. industrial robotics) are provided. Ideal for students and practitioners, this book provides readers with a clear path to understanding rigid body mechanics and its significance in numerous sub-fields of mechanical engineering and related areas.

Spis treści

1 Preliminary on vector, matrix, complex number and quaternion

1.1 Vector

1.1.1 Definition

1.1.2 Operations

1.2 Matrix

1.2.1 Definition

1.2.2 Operations

1.3 Complex number

1.3.1 Definition

1.3.2 Operations

1.4 Quaternion

1.4.1 Definition

1.4.2 Operations

1.4.3 Some definitions and relations

1.5 Special vectors, matrices and terms

2 Orientation and position representation

2.1 Coordinate frames

2.2 Observation frame, description frame and vector notations

2.3 Orientation

2.3.1 Rotation matrix

2.3.2 Equivalent/effective axis and angle

2.3.3 Exponential coordinates

2.3.4 Active / passive interpretations of rotation matrix and orientation from successive rotations

2.3.5 Euler angles

2.3.6 RPY angles

2.3.7 Quaternion of rotation

2.3.8 Cayley-Klein matrix

2.4 Position

2.4.1 Position of a rigid body and position of a point

2.4.2 Passive and active representation of position

2.5 Examples

3 Velocity and acceleration

3.1 Angular velocity

3.1.1 Angular velocity derived from rotation matrix

3.1.2 Angular velocity and the time derivative of a vector fixed in the body frame

3.1.3 Angular velocity derived from Euler angles and RPY angles

3.1.4 Angular velocity derived from equivalent/effective axis and angle

3.1.5 Angular velocity derived from quaternion of rotation

3.1.6 Angular velocity for successive rotations

3.2 Linear velocity

3.3 Acceleration

3.3.1 Angular acceleration

3.3.2 Linear acceleration

3.4 Examples

4 Dynamics

4.1 Inertial Properties

4.1.1 Inertial properties for linear motion

4.1.2 Inertial properties for angular motion

4.1.3 Inertia ellipsoid

4.1.4 Example

4.1.5 Theorems and rules

4.1.6 Examples

4.2 Momentum

4.2.1 Linear momentum

4.2.2 Angular momentum

4.2.3 Examples

4.3 Force, moment of force and torque

4.4 impulse, work and power

4.5 Mechanical energy

4.5.1 Kinetic energy

4.5.2 Potential energy

4.5.3 Mechanical energy

<4.5.4 Examples

O autorze

Dr. Loulin Huang is Associate Professor of Mechanical Engineering at Auckland University of Technology in New Zealand. His research interests include Mechatronics, Robotics, and Dynamics and Control.

Blurb

This updated second edition broadens the explanation of rotational kinematics and dynamics — the most important aspect of rigid body motion in three-dimensional space and a topic of much greater complexity than linear motion. It expands treatment of vector and matrix, and includes quaternion operations to describe and analyze rigid body motion which are found in robot control, trajectory planning, 3D vision system calibration, and hand-eye coordination of robots in assembly work, etc. It features updated treatments of concepts in all chapters and case studies.

The textbook retains its comprehensiveness in coverage and compactness in size, which make it easily accessible to the readers from multidisciplinary areas who want to grasp the key concepts of rigid body mechanics which are usually scattered in multiple volumes of traditional textbooks. Theoretical concepts are explained through examples taken from across engineering disciplines and links to applications and more advanced courses (e.g. industrial robotics) are provided.

Ideal for students and practitioners, this book provides readers with a clear path to understanding rigid body mechanics and its significance in numerous sub-fields of mechanical engineering and related areas.

• Streamlines the treatment of rigid body motions in; one-, two, or three-dimensional spaces within an unified mathematical framework supported with vector, matrix, and quaternion operations;
• Maximizes reader understanding of analysis of rotational kinematics and dynamics;
• Explains theoretical concepts through examples taken from across engineering disciplines and provides linkages to applications and more advanced courses (e.g. industrial robotics);
• Features updated treatments of concepts in all chapters and case studies.