Theory of Gearing: Kinematics, Geometry, and Synthesis (Hardback) book cover

Theory of Gearing

Kinematics, Geometry, and Synthesis

By Stephen P. Radzevich

© 2013 – CRC Press

743 pages | 513 B/W Illus.

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Paperback: 9781138075894
pub: 2017-03-29
Hardback: 9781466514485
pub: 2012-07-19
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pub: 2012-07-19
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The first book of its kind, Theory of Gearing: Kinematics, Geometry, and Synthesis systematically develops a scientific theory of gearing that makes it possible to synthesize novel gears with the desired performance. Written by a leading gearing expert who holds more than 200 patents, it presents a modern methodology for gear design.

The proposed theory is based on a key postulate: all the design parameters for an optimal gear pair for a particular application can be derived from (a) a given configuration of the rotation vectors of the driving and driven shafts and (b) the power transmitted by the gear pair. This allows engineers to synthesize the desired gear pairs with only the following input information:

  • The rotation and torque on the driving shaft
  • The configuration of the driven shaft in relation to the driving shaft
  • The desired rotation and torque of the driven shaft

Beginning with the fundamentals, the book reconsiders the basic theory of kinematics and geometry of gears to provide a sound basis for the evaluation and development of future designs. It then examines ideal and real gearing for parallel-axis, intersected-axis, and crossed-axis gearing. The book addresses how to minimize vibration and noise in gears, discusses aspects of implementing the theory of gearing, and analyzes principal features of power transmission and the loading of gear teeth. More than 500 figures clearly illustrate the principles.

This is an invaluable resource for engineers and researchers who work in gear design, gear production, and the application of gears as well as for students in mechanical and manufacturing engineering. Covering all known gear designs, this book offers an analytical solution to the problem of designing optimal gear pairs for any given application. It also encourages researchers to further develop the theory of gearing.


The text is clear and rich in details … well done; starting with a ‘Synthesis’ makes sense and offers the chance to introduce the topic smoothly.

—Hellmuth Stachel,Vienna University of Technology, Austria

… This book is starting to touch on areas that need more discussion such as the tooth curvature and how the force vectors are calculated and used in continued analysis. I like how it starts at a lower level then builds into the real geometry of the tooth surface and how this can effect the gear meshing.

—Todd Smith, Global Director Gear Engineering & Manufacturing, Dana Holding, Maumee, Ohio, USA

Table of Contents


Kinematics of a Gear Pair

Geometry of Gear Tooth Flanks: Preliminary Discussion

Geometry of Contact of Tooth Flanks of Two Gears in Mesh

Concept of Synthesis of a Gear Pair with Prescribed Performance

Ideal Gearing: Parallel-Axis Gearing

Involute Gearing

Noninvolute Gearing

High-Conforming Parallel-Axis Gearing

Synthesis of Optimal Parallel-Axis Gearing

Ideal Gearing: Intersected-Axis Gearing

Geometrically Accurate Intersected-Axis Gear Pairs

High-Conforming Intersected-Axis Gearing

Ideal Gearing: Crossed-Axis Gearing

Geometrically Accurate Crossed-Axis Gearing: R-Gearing

High-Conforming Crossed-Axis Gearing

Ideal (Geometrically Accurate) Two-Degree-of-Freedom Gearing

Kinematics, Geometry, and Design Features of 2-DOF Gearing

Real Gears and Their Application: Real Gearing

Desired Real Gearing: Spr-Gearing

Approximate Real Gearing

Generic Gear Shape

Gear Noise

Real Gears and Their Application: Gear Trains

Gear Ratio of a Multistage Gear Drive

Split Gear Drives

Real Gears and Their Application: Principal Features of Power Transmission and Loading of the Gear Teeth

Local Geometry of the Interacting Tooth Flanks

Contact Stresses in Low-Tooth-Count Gearing

Application of the Results Derived from Theory of Gearing


Appendix A: Elements of Coordinate Systems Transformations

Appendix B: Novikov’s Gearing Invention Disclosure

Appendix C: Wildhaber’s Gearing Invention Disclosure

Appendix D: Engineering Formulas for the Specification of Gear Tooth Flanks

Appendix E: Change of Surface Parameters

Appendix F: Notations

Appendix G: Glossary




About the Author

Dr. Stephen P. Radzevich is a professor of mechanical engineering and manufacturing engineering. He has extensive industrial experience in gear design and manufacture and has developed numerous software packages dealing with computer-aided design (CAD) and computer-aided manufacturing (CAM) of precise gear finishing for a variety of industrial sponsors. Dr. Radzevich has spent over 35 years developing software, hardware, and other processes for gear design and optimization. Besides his industry work, he trains engineering students at universities and gear engineers in companies. He has authored and coauthored over 30 monographs, handbooks, and textbooks, including Kinematic Geometry of Surface Machining (CRC Press, 2007), Gear Cutting Tools: Fundamentals of Design and Computation (CRC Press, 2010), and Dudley’s Handbook of Practical Gear Design and Manufacture (CRC Press, 2012). He has also authored and coauthored over 250 scientific papers and holds more than 200 patents on inventions in the field.

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Mechanics / General
TECHNOLOGY & ENGINEERING / Industrial Design / General