Theory of Gearing

This comprehensive fourth edition of Stephen P. Radzevich’s acclaimed work presents a thorough exploration of gear theory, offering both theoretical foundations and practical applications for engineers and researchers working with gear design and manufacturing.

The fourth edition has been meticulously revised with the entire manuscript thoroughly updated to enhance clarity and precision. Many illustrations have been completely replaced with superior versions, and numerous new illustrations have been added throughout the text. The equivalent pulley‑and‑belt transmission concept has been significantly developed and refined, and the author has incorporated an important new result in envelope theory – a contribution valuable not only to gear theory but also to pure mathematics in the field of differential geometry of surfaces. Additionally, this edition includes the latest advances in gear theory from the beginning of the twenty‑first century, ensuring readers have access to cutting‑edge developments in the field.

This book is essential reading for mechanical engineers, automotive engineers, manufacturing engineers, researchers, and graduate students seeking to master the science of modern gear design.

Stephen P. Radzevich is a Professor of Mechanical Engineering and a Professor of Manufacturing Engineering. He earned an MSc in 1976, a PhD in 1982, and a Dr(Eng)Sc in 1991, all in Mechanical Engineering. Dr. Radzevich has extensive industrial experience in gear design and gear manufacture. He has developed numerous software packages dealing with computer-aided design (CAD) and computer-aided machining (CAM) of precise gear finishing for a variety of industrial sponsors. His main research interest is in the field of kinematics and geometry of gearing, particularly with a focus on precision gear design, high-power-density gear trains, torque share in split power transmission systems (SPTS), design of special-purpose gear cutting/finishing tools, and design and machine (finish) of precision gears for low-noise and noiseless transmissions of cars, light trucks, and so forth.

Dr. Radzevich has spent about 50+ years developing software, hardware, and other processes for gear design and optimization. Besides his work for industry, he trains engineering students at universities and gear engineers in companies.

He has authored or coauthored over 50 monographs, handbooks, and textbooks. The monographs Generation of Surfaces (2001), Kinematic Geometry of Surface Machining (2007, 2nd ed. 2014), CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: The DG/K-Based Approach (2008), Gear Cutting Tools: Fundamentals of Design and Computation (2010, 2nd ed. 2017), Precision Gear Shaving (2010), Dudley’s Handbook of Practical Gear Design and Manufacture (2nd ed. 2012, 3rd ed. 2016, 4th ed. 2021), High-Conformal Gearing: Kinematics and Geometry (2016; 2nd ed. 2020), Theory of Gearing: Kinematics, Geometry, and Synthesis (2012, 2nd ed. 2018, 3rd ed. 2022), Geometry of Surfaces: A Practical Guide for Mechanical Engineers (2013, 2nd ed. 2019), Recent Advances in Gearing – Scientific Theory and Applications (2021), and Gear Accuracy – A Treatise on Gear Noise Excitation, Vibration Generation, and Dynamics of Operation (2025) are among his recently published volumes. He also authored or coauthored over 700 scientific papers and holds over 260 patents on inventions in the field (USA, Japan, Russia, Europe, Canada, Soviet Union, South Korea, Mexico, and others).