Title: *Fundamentals of Robot Mechanics*

Author: Gregory L. Long

Binding: Hardcover

Page Count: 645

Language: English

Publisher: Quintus-Hyperion Press

Year: 2015

ISBN-13: 978-0-9861094-1-6

Dimensions: 10.25 x 8.25 x 1.75 (inches)

The Fundamentals of Robot Mechanics contains a thorough treatment of essential concepts in robot mechanics. Beginning with elementary topics taught in college physics and first-semester calculus, this thoughtful textbook conveys an in-depth presentation of rotation transformations, homogeneous transformations, Denavit-Hartenberg parameters, forward kinematics, inverse kinematics, instantaneous kinematics/statics using screws, singularity analysis, and dynamics of serial-chain robot manipulators.

- This exposition of robot fundamentals provides the following:
- Step-by-Step instructions for finding the classic DH Parameters.
- A computationally efficient formulation of serial-chain forward and inverse kinematics.
- An elegant and computationally efficient formulation for the manipulator Jacobian using screw theory.
- A concise treatment of statics using virtual work and screw theory.
- A broad treatment of singular configurations using screw theory.
- Workspace analysis techniques for 2-revolute and 3-revolute pair serial-chain structures.
- A complete and computationally efficient formulation of manipulator dynamics using Lagrange's equations and dynamic constants.
- Design guidelines that simplify the equations-of-motion for serial-chain manipulators.

The Fundamentals of Robot Mechanics contains over 470 color illustrations, over 100 detailed single and extended examples, and over 260 exercises to promote mastery of both theory and practice. This text also includes references for over 200 research articles, textbooks, and other resources. A professional-trade book for all robotics students and practicing engineers who wish to master the concepts in robot mechanics.

**1 INTRODUCTION**

1.1 Introduction

1.2 Programmable Manipulators and Machine Tools

1.3 Early Teleoperated Systems

1.4 The Emergence of Computer Numerical Control

1.5 Robot Manipulators on the Production Line

1.6 The Science of Manipulator Mechanics

1.7 Modern Robot Manipulators

1.8 Lower Kinematic Pairs

1.9 Kinematic Pairs and Manipulator Structures

1.10 Summary

References and Suggested Reading

**2 RIGID BODY TRANSFORMATIONS**

2.1 Introduction

2.2 Cartesian Coordinate Systems

2.3 Referencing Points Relative to Multiple Frames

2.4 Resolving Vectors

2.5 The Direction Cosines Matrix

2.6 Rotation Operators

2.7 Rotation Operator/Orientation Matrix

2.8 Principal Rotation Matrices

2.9 Composite Rotations

2.10 Non-Commutability of Spatial Rotations

2.11 Absolute Rotation Angles---Roll, Pitch, Yaw

2.12 Relative Rotation Angles (Euler Angles)

2.13 Rotation Angle/Rotation-Axis Vector Extraction

2.14 Homogeneous Transformations

2.15 Quaternions

2.16 Summary

Nomenclature

References and Suggested Reading

Exercises

**3 FORWARD KINEMATICS**

3.1 Introduction

3.2 Commonly Used Coordinate Frames

3.3 Denavit-Hartenberg Parameters

3.4 Kinematic Skeletons

3.5 2R Planar Manipulator

3.6 Offset Articulate Manipulator

3.7 Offset Spherical Manipulator

3.8 Manipulators with Four-Bar Sub-Chains

3.9 Summary

Nomenclature

References and Suggested Reading

Exercises

**4 INVERSE KINEMATICS**

4.1 Introduction

4.2 End-Effector Position and Orientation

4.3 End-Effector/Tool Closure Equation

4.4 Inverse Trigonometric Functions

4.5 Geometric Method: Overview

4.6 2R Planar Manipulator: Geometric Solution

4.7 Offset Articulate Regional: Geometric Solution

4.8 Offset Spherical Regional: Geometric Solution

4.9 Orientation Structure: Geometric Solution

4.10 Algebraic Method: Overview

4.11 2R Planar Manipulator: Algebraic Solution

4.12 Offset Articulate Manipulator: Algebraic Solution

4.13 Offset Spherical Manipulator: Algebraic Solution

4.14 General Solutions

4.15 Summary

Nomenclature

References and Suggested Reading

Exercises

**5 INSTANTANEOUS KINEMATICS**

5.1 Introduction

5.2 Relative Velocities

5.3 Screw Coordinates

5.4 The Manipulator Jacobian

5.5 Resolving Joint-Screws in Specific Link Frames

5.6 2R Planar Manipulator

5.7 Offset Articulate Manipulator

5.8 Offset Spherical Manipulator

5.9 Summary

Nomenclature

References and Suggested Reading

Exercises

**6 STATICS**

6.1 Introduction

6.2 Fundamental Notions

6.3 A Wrench on a Screw

6.4 Transferring a Wrench

6.5 The Principle of Virtual Work

6.6 The Virtual Product

6.7 Joint Torques/Forces for Static Equilibrium

6.8 Duality: Instantaneous Kinematics and Statics

6.9 Summary

Nomenclature

References and Suggested Reading

Exercises

**7 SINGULARITIES**

7.1 Introduction

7.2 Jacobian Rank

7.3 Matrix of Jacobian Cofactors

7.4 Reciprocal Screws as the Matrix of Cofactors

7.5 Offset Spherical Manipulator

7.6 Offset Articulate Manipulator

7.7 Manipulators with Less Than Six DOF

7.8 2R Planar Manipulator

7.9 3R Spatial Manipulator

7.10 Summary

Nomenclature

References and Suggested Reading

Exercises

**8 WORKSPACE**

8.1 Introduction

8.2 Workspace: 2R Manipulator Geometries

8.3 Workspace: 3R Manipulator Geometries

8.4 Extreme Distances

8.5 Summary

Nomenclature

References and Suggested Reading

Exercises

**9 DYNAMICS**

9.1 Introduction

9.2 Energy Relations for a Mass Particle

9.3 Energy Relations for a Rigid Link

9.4 Link Inertia Matrix

9.5 D'Alembert's Principle

9.6 Generalized Coordinates/Forces

9.7 Lagrange's Equations

9.8 2P Planar Manipulator

9.9 2R Planar Manipulator

9.10 Properties of the Manipulator Inertia Matrix

9.11 Characteristics Due to Joint Interaction

9.12 The Lagrange-Christoffel Formulation

9.13 Christoffel Symbol Uniqueness

9.14 Offset Spherical Regional Structure

9.15 Offset Articulate Regional Structure

9.16 Newton-Euler Method

9.17 Newton-Euler Subroutines

9.18 Summary

Nomenclature

References and Suggested Reading

Exercises

**A MATRICES AND LINEAR VECTOR SPACES**

A.1 Matrices

A.2 Partitioned Matrix

A.3 Diagonal Matrix

A.4 Matrix Addition

A.5 Matrix Multiplication

A.6 Frequently Used Inverses

A.7 Real Vector Spaces

A.8 Manipulator Inertia Matrix: Properties/Proofs

References and Suggested Reading

**B TRIGONOMETRIC FORMULAS**

**C INERTIAL PARAMETER DETERMINATION**

C.1 Inertial Parameter Determination

C.2 Rotation of Axes

References and Suggested Reading

**D CHRISTOFFEL SYMBOL TABULATIONS**

D.1 Christoffel Symbols for n = 2

D.2 Christoffel Symbols for n = 3

D.3 Christoffel Symbols for n = 4

D.4 Christoffel Symbols for n = 5

D.5 Christoffel Symbols for n = 6

**AUTHOR INDEX**

**SUBJECT INDEX**

Please visit www.RobotMechanicsControl.info for textbook examples that use MATLAB and Mathematica CAS software.