From the Preface:

As a teacher of Orthodontic Biomechanics, my primary objective is to assist students in understanding how a rational biomechanic approach, premised on fundamental Mathematics and Physics, can improve projected outcomes for various orthodontic treatments. While predicting dental movement with absolute certainty may be a theoretical impossibility, my clinical experience has been that a “rational approach” offers superior predictive capacity, enabling clinicians to anticipate outcomes with a high degree of confidence on a routine basis. Because of the inherent vagaries in any biological system, minor deviations from anticipated outcomes, that bear no significant impact on clinical effect, are to be expected. However, I have realized that when substantial differentials between observed and anticipated outcomes are observed, they invariably seem to be rooted in one or more of the following: 1) incorrect estimation of the center of resistance (CR) or the value of the needed M/F (note: determining these values with good accuracy can be sometimes difficult); 2) incorrect evaluation of the effects of occlusal forces, 3) incorrect calculations; 4) application of a force system that does not correspond to what has been calculated. In order to determine the source and nature of their errors, I teach students to retrace the steps in their biomechanic analyses. When errors are identified, students can easily make corrections and adjust mechanics accordingly to achieve optimal results. I feel compelled to emphasize that proper clinical application of biomechanic theory requires a solid grounding in an academic background of Mathematics, Physics, and Biology.

I have dedicated the last 30 years of my life to developing and teaching orthodontic biomechanics. During my tenure as a teacher, one of the most frequent requests from students has been for learning tools that test both their knowledge and their ability to apply it. In my early teaching years, I presented spontaneous exercises to students during lectures. These, however, evolved into more complex problems as students became increasingly engaged. Their probing questions offered me insight into their learning process and began to shape the types of exercises that I prepared to help future students learn more effectively. The collection of exercises in this book are derived from these sessions with my students. It is my hope that future editions of this book contain a broader range of exercises, that reflect an even greater contribution from my past students. I also look forward to continuing input from colleagues from the Biomede group, who share my dedication to teaching orthodontic biomechanics worldwide.
This textbook is a valuable learning tool intended as ancillary material for students actively engaged in learning Orthodontic Biomechanics. It does not offer information on basic prerequisites and assumes that users have acquired enough knowledge of the fundamental principles of Biomechanics.
References to essential formulas and basic procedures for solving problems have been added, however, in the first section of this book for convenience.
For a proper introduction to orthodontic biomechanics, we redirect the reader in the last section of this book to a variety of excellent textbooks that have been published, including the online multimedia textbook referenced earlier, “Biomechanics in Orthodontics” that I published with colleague Prof. Birte Melsen.
I would like to thank my coauthors, past students and Biomede members, Dr. Wislei Oliveira, Dr. Paola Merlo and Dr. Siva Vasudavan for participating in efforts to bring this book to fruition. I also offer sincere gratitude to Dr. Andrea Boggio for his assistance in preparing this manuscript.
Finally, I offer a special thank you to all those who invested time and energy in teaching me. This book honors them and reflects my best efforts to extend their legacies well into the future.

Giorgio Fiorelli
Arezzo, May 2019