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SolutionManual
Theory of Applied Robotics
Kinematics, Dynamics, and Control
Reza N. Jazar
Department of Mechanical Engineering
Manhattan College, Riverdale, NY 10471
January 2, 2008
,ii
, This is page iii
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Contents
1 Introduction 1
2 Rotation Kinematics 5
3 Orientation Kinematics 35
4 Motion Kinematics 73
5 Forward Kinematics 117
6 Inverse Kinematics 151
7 Angular Velocity 165
8 Velocity Kinematics 183
9 Numerical Methods in Kinematics 207
10 Acceleration Kinematics 219
11 Motion Dynamics 235
12 Robot Dynamics 263
13 Path Planing 273
14 F Time Optimal Control 309
15 Control Techniques 331
,iv
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Preface
This book is the solution manual for the textbook entitled "Theory of Ap-
plied Robotics: Kinematics, Dynamics, and Control". Knowing that mathe-
matical oriented problems, such as the problems in Robotics, may be solved
in different ways, the provided solutions might not be the best. The author
appreciate if the instructors and readers of this solution manual inform
him about a better or simpler solution for any one of the problems. Also,
the author appreciate if the readers inform him about any mistake in the
solutions or in the book.
The textbook is designed to serve as a text for engineering students.
It introduces the fundamental knowledge used in robotics. This knowledge
can be utilized to develop computer programs for analyzing the kinematics,
dynamics, and control of robotic systems.
Level of the Textbook
The textbook is addressed primarily to the last year of undergraduate
and the first year graduate students in engineering. This book provides
both fundamental and advanced topics on the kinematics and dynamics of
robots. The whole book can be covered in two successive courses however,
it is possible to jump over the asterisks sections and cover the book in one
course. The students are required to know the fundamentals of kinematics
and dynamics, as well as a basic knowledge of numerical methods.
The contents of the book have been kept at a fairly theoretical-practical
level. Many concepts are deeply explained and their use emphasized, and
most of the related theory and formal proofs have been explained. Through-
out the book, a strong emphasis is put on the physical meaning of the con-
cepts introduced. Topics that have been selected are of high interest in the
field. An attempt has been made to expose the students to a broad range
of topics and approaches.
Organization of the Textbook
The text is organized so it can be used for teaching or for self-study.
Chapter 1 “Introduction,” contains general preliminaries with a brief review
of the historical development and classification of robots.
Part I “Kinematics,” presents the forward and inverse kinematics of
robots. Kinematics analysis refers to position, velocity, and acceleration
analysis of robots in both joint and base coordinate spaces. It establishes
Printer: Opaque this
SolutionManual
Theory of Applied Robotics
Kinematics, Dynamics, and Control
Reza N. Jazar
Department of Mechanical Engineering
Manhattan College, Riverdale, NY 10471
January 2, 2008
,ii
, This is page iii
Printer: Opaque this
Contents
1 Introduction 1
2 Rotation Kinematics 5
3 Orientation Kinematics 35
4 Motion Kinematics 73
5 Forward Kinematics 117
6 Inverse Kinematics 151
7 Angular Velocity 165
8 Velocity Kinematics 183
9 Numerical Methods in Kinematics 207
10 Acceleration Kinematics 219
11 Motion Dynamics 235
12 Robot Dynamics 263
13 Path Planing 273
14 F Time Optimal Control 309
15 Control Techniques 331
,iv
, This is page v
Printer: Opaque this
Preface
This book is the solution manual for the textbook entitled "Theory of Ap-
plied Robotics: Kinematics, Dynamics, and Control". Knowing that mathe-
matical oriented problems, such as the problems in Robotics, may be solved
in different ways, the provided solutions might not be the best. The author
appreciate if the instructors and readers of this solution manual inform
him about a better or simpler solution for any one of the problems. Also,
the author appreciate if the readers inform him about any mistake in the
solutions or in the book.
The textbook is designed to serve as a text for engineering students.
It introduces the fundamental knowledge used in robotics. This knowledge
can be utilized to develop computer programs for analyzing the kinematics,
dynamics, and control of robotic systems.
Level of the Textbook
The textbook is addressed primarily to the last year of undergraduate
and the first year graduate students in engineering. This book provides
both fundamental and advanced topics on the kinematics and dynamics of
robots. The whole book can be covered in two successive courses however,
it is possible to jump over the asterisks sections and cover the book in one
course. The students are required to know the fundamentals of kinematics
and dynamics, as well as a basic knowledge of numerical methods.
The contents of the book have been kept at a fairly theoretical-practical
level. Many concepts are deeply explained and their use emphasized, and
most of the related theory and formal proofs have been explained. Through-
out the book, a strong emphasis is put on the physical meaning of the con-
cepts introduced. Topics that have been selected are of high interest in the
field. An attempt has been made to expose the students to a broad range
of topics and approaches.
Organization of the Textbook
The text is organized so it can be used for teaching or for self-study.
Chapter 1 “Introduction,” contains general preliminaries with a brief review
of the historical development and classification of robots.
Part I “Kinematics,” presents the forward and inverse kinematics of
robots. Kinematics analysis refers to position, velocity, and acceleration
analysis of robots in both joint and base coordinate spaces. It establishes
