Reza N. Jazar - Theory of Applied Robotics: Kinematics, Dynamics, and Control, 3rd Edition

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Ten years have passed since the second edition of Theory of Applied Robotics has been published. The second edition of the book has been strongly accepted in academia for research and teaching. Many universities and colleges adopted this book as a teaching text or as a reference. The book also had great success in Chinese universities, especially after its Chinese translation was officially published by Springer in 2018. During the past 10 years, I have received many constructive comments from all around the world, from colleagues, friends, instructors, researchers, and students. In this third edition, I used those comments to improve the text as well as remove typos and numerical errors. Further, I tried to make the third edition more educational and clearer to make the book more suitable for self-training.

The key concept of robotics kinematics and dynamics is the understanding of the coordinate frame transformation, a topic that Theory of Applied Robotics is covering in the best possible way. We begin this topic by analyzing rotation about a principal axis of global and body coordinate frames. Rotation about an arbitrary axis is the next step. Understanding of rotation about an arbitrary axis is the best way to study kinematics of robots. We will show how to break such a complicated rotation into a series of principal rotations to develop the required mathematical relations by a series of simple steps. To make it possible, we will show how we may introduce extra dummy coordinate frames to simplify moving from initial to final coordinate frame by a modular and structural process. Auxiliary coordinate frames is a unique concept that has been added to the kinematic knowledge body of robot kinematics by this book. Readers of this book will become masters in using this scientific trick in kinematic analysis.

The robot kinematics will be continued by covering the first and second time derivatives of rotation transformation mathematics. The first derivative introduces the complicated and strange concept of angular velocity. Angular velocity is a complicated concept because we do not have any unique mathematical quantity whose time derivative will be angular velocity. Angular velocity is a vectorial quantity, but it is not time derivative of another scalar or vectorial physical quantity. This fact makes angular velocity appear as a new individual concept. It, however, will be connected to a combination of time derivative of rotation transformation matrices. The appearance of rotation transformation matrices in the definition of angular velocity gives us the ability to define time derivative operations in different coordinate frames. Therefore, we will see that there are several different velocities all mathematically correct but not all sensible. The second derivative and introduction of acceleration kinematics make this concept more complicated such that we will be able to define and calculate greater accelerations than those we work with. The freedom of taking a vectorial physical quantity from one coordinate frame and taking derivative in another coordinate and still expressing in a third coordinate frame helped me discover a new acceleration called Razi acceleration (Jazar 2011; Harithuddin et al. 2015).

My intention in this book is to explain robotics in a manner I would have liked to be explained to me as a student. This book can now help students by being a great reference that covers all aspects of robotics and that provides students with detailed explanations and information.