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).

1. Non-Involute Gearing: Basics. Part I: Fundamentals. 2. Principal Kinematics of Gear Pair. 3. Principal Planes and Main Reference Systems Associated with Gear Pair. 4. Smooth Transmission of Uniform Rotary Motion: Three Fundamental Laws of Gearing. 5. Permissible Variation of the Design Parameters in Equivalent Pulley-and-Belt Transmission. Part II: Geometrically Accurate Gearing. Section II-A: Geometrically Accurate Gearing: Parallel-Axes Gearing. 6. Involute Gearing: Kinematics and Geometry. 7. Simplified Approach for Generation of Involute Gear Tooth Flank. 8. Parallel-Axes Involute Gearing of Special Design. 9. Gear Tooth Profile Modification: Generating Rack Shift. 10. Interaction of Tooth Flanks in Parallel-Axes Involute Gearing. 11. Novikov/Conformal and High-Conformal Gearing. Section II-B: Geometrically Accurate Gearing: Intersected-Axes Gear Pairs. 12. Geometrically Accurate Intersected-Axes Gear Pairs. 13. Interaction of Tooth Flanks in Geometrically Accurate Intersected-Axes Gearing. Section II-C: Geometrically Accurate Gears: Crossed-Axes Gearing. 14. Geometrically Accurate Crossed-Axes Gear Pairs: R-Gearing. 15. Interaction of Gears in Geometrically Accurate Crossed-Axes Gearing. 16. Geometrically Accurate Worm-Gearing: Peculiarities of Kinematics and Geometry. Part III: Geometrically Accurate Real Gears: Kinematics, Geometry, and Application. 17. Geometrically Accurate Real Gearing: Spr-Gear System. Part IV: C-üVariable Gearing. 18. C-üvar Gears: Kinematics, Geometry, and Novel Concept to Design Geometrically Accurate Gears. Part V: On Synthesizing of Favorable Geometrically Accurate Gear Pairs. 19. Features of Contact Geometry. Part VI: Real Gears and Their Application. 20. Generic Gear Surfaces. 21. Approximate Real Gearing. 22. Local Geometry of Interacting Gear Tooth Flanks. 23. Strength of Gear Teeth. 24. SPTS - Split Power Transmission Systems. 25. Vector Approach in Kinematic and Dynamic Analysis of Complex Gear Transmission Systems. 26. Gear Ratio of Multistage Gear Transmission System. 27. Gear Accuracy. 28. Gear Noise and Vibration. 29. Design Peculiarities of Geometrically Accurate and Almost Geometrically Accurate Gears. 30. A Brief Overview on Evolution of the Scientific Theory of Gearing.