Asymmetric Gearing: 1st Edition (Hardback) book cover

Asymmetric Gearing

1st Edition

By Alexander L. Kapelevich

CRC Press

271 pages | 330 B/W Illus.

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Hardback: 9781138554443
pub: 2018-09-17
eBook (VitalSource) : 9781315149011
pub: 2018-08-06
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The history of gears with asymmetric teeth is not sufficiently recorded in modern gear literature, with some gear researchers concluding that asymmetric tooth gears were discovered just several decades ago. This book sheds light upon the origins and state of asymmetric gearing, referencing technical articles from the 19th, 20th, and 21st centuries. As a practicing gear engineer with over 40 years’ experience, author Alexander L. Kapelevich has successfully implemented asymmetric gears in a variety of custom gear transmissions. This book addresses all aspects of asymmetric gear development, including theoretical fundamentals; tooth geometry optimization; stress analysis and rating; design and production specifics; analytical and experimental comparison to the best symmetric gears; and application examples. Readers are encouraged to look beyond the status quo established by traditional gear design, and to apply principles of asymmetric gearing to actual gear design. Optimal solutions are presented for gear drives that will maximize technical performance and marketability.


  • Presents a state-of the-art, comprehensive historical overview of asymmetric gearing
  • Explains the Direct Gear Design® approach to asymmetric gear design
  • Describes asymmetric tooth gear geometry optimization, areas of existence, and parameter selection limits
  • Considers practical aspects of asymmetric gear fabrication and measurement
  • Presents analytical and experimental comparison of asymmetric gears to advanced symmetric gears, showing the advantages of asymmetric designs
  • Provides numerous real-world examples of asymmetric gear application


"This book covers the development stages of asymmetric gear trains, progressing from theory through analysis, manufacturing, and final applications. The author shows the benefits of the asymmetric mesh and includes practical recommendations for gear fabrication. This material can be useful for new gearbox designs as well as for applications where higher gearbox torque capabilities are required within limited existing envelopes. Overall, this new work will offer helpful information for multiple generations of engineers."

—Yuriy Gmirya, Sikorsky Aircraft Corporation, a Lockheed Martin Company, USA

"Alexander Kapelevich has written a treatise that is destined to be the classic work on asymmetric gearing. This book is comprehensive and gives engineers the tools they need to understand and design asymmetric gears, which have many advantages such as maximum power density, maximum efficiency, and minimum noise and vibration. It clearly explains the method of Direct Gear Design®, which is easy to understand for anyone familiar with involute gears. The many example gear sets and design charts give comprehensive design guidelines that show the way forward to advance state-of-the-art gear design."

Robert Errichello, GEARTECH, Montana, USA

"An author of this book is well known as a researcher and implementor of asymmetric gears for over 30 years. His book Asymmetric Gearing reflects his experience in this area and covers virtually all aspects of the development of this type of gears, from a historical overview and a current state of the art to the latest applications. It also contains a comprehensive bibliography of publications on this subject. This book is written in a plain understandable style intending to be an eye-opener for gear engineers who are willing to look beyond standards and established traditional gear design practice to achieve the competitive performance of their products. In my opinion, this book will allow moving forward the field of Gearing and will be useful for industry experts, researchers, and students."

—Veniamin I. Goldfarb, Institute of Mechanics, Izhevsk State Technical University, Izhevsk, Russia

"People look for books on gear engineering, but there is no sufficient information about the detailed problem of gears with asymmetric tooth form. The book authored by Dr. Alex Kapelevich on the gear of asymmetric tooth form is the first comprehensive book on this matter. Dr. Kapelevich was educated in the Soviet Union, where many mathematicians who can deal with gear problems were active. He designed gears with asymmetric tooth form for aircraft gears with big success. I believe without a doubt, that he is the first man in this field of technology on gears with asymmetric tooth form. This book contains much of his experience. I recommend this book for gear engineers who are interested in gears with asymmetric tooth form."

—Aizoh Kubo, Kubo's Gear Technologies, Kyoto, Japan

"This is a very comprehensive book on the subject of asymmetric gearing, it touches on the history and then gets deeply technical on the design aspects with many design examples for the reader to follow along and learn. It also explains how to manufacture and measure the gears which are very important since designing them alone is only half the job. Dr. Kapelevich also covers tolerancing, efficiency, and side by side comparisons of symmetric and asymmetric gear designs. Altogether it is very complete, a definitive work by Dr. Kapelevich that is well timed since the industry is heading towards more optimized and power dense designs."

— Anders Flodin, Höganäs AB, Sweden

"Alexander Kapelevich's newest book deals with a topic, which seems to be underrated, today: Asymmetric Gearing. The book offers both, a comprehensive overview as well as thoroughly researched information about the latest state of technology along the complete process chain of asymmetric gears. With many useful explanations and recommendations for the practical application of asymmetrical gears - from gear geometry over limits, rating to manufacturing, tolerancing and inspections - this book offers a lot of valuable information not only about asymmetric but also general aspects of gears and is a meaningful addition to the book "Direct Gear Design" of the same author."

Karsten Stahl, Technische Universität München, Germany

" Asymmetric Gears have been well known in the gear industry for many years but have not been used very often in practical gear design. Maybe the reason for that is a lack of knowledge and missing of detailed description/specification, standards, and computer programs. This book can help to understand asymmetric gearing much better and to use the advantages in special applications in which the higher loaded drive flank can be optimized ". Also, manufacturing and measurement data have to be calculated and provided to the shop. Nevertheless, some education at universities and of the staff in gear companies will also be necessary if more acceptance of asymmetric gearing should be achieved."

— Franz J. Joachim, Joachim Gear Consulting (before retirement: ZF Friedrichshafen AG), Germany

"A new book by Dr. Alex Kapelevich "Asymmetric Gearing" is the first book ever on the subject, and even only due to this, the book can be considered as a significant event in the gear community of the United States. Besides gears with asymmetric teeth are known for a long while, there was no a source of information for the gear engineers, in which the topic is covered. In his book, Dr. A. Kapelevich has summarized his tremendous experience and knowledge on asymmetric gear drives. No doubt the book will find its readers in a short while."

— Stephen P. Radzevich, Ph.D., Dr.Sci., Professor (retired), Mechanical Engineering, USA

Table of Contents

1. History of Asymmetric Gears and Modern State of Art

2. Macrogeometry of Asymmetric Tooth Gears

3. Area of Existence

4. Asymmetric Gearing Limits

5. Gear Geometry Optimization

6. Stress Analysis and Rating of Asymmetric Gears

7. Special Types of Asymmetric Gears

8. Tolerancing and Tolerance Analysis

9. Asymmetric Gear Manufacturing

10. Symmetric vs. Asymmetric Gears

11. Asymmetric Gear Applications

About the Author

Dr. Alexander L. Kapelevich is a gear design consultant at AKGears, LLC. He holds a Master’s Degree in Mechanical Engineering at Moscow Aviation Institute and a Ph.D. Degree in Mechanical Engineering at Moscow State Technical University. Dr. Kapelevich has over 40 years of gear transmission research and design experience. He began his career working in the Russian Aviation Industry, where he was involved in R&D, software development, testing, and failure investigation for aerospace gear transmissions. Living in the USA since 1994, he developed the Direct Gear Design methodology for custom gear transmissions which have been implemented in various fields such as aerospace, automotive, agriculture, defense, robotics, racing, and many others. His specialty is the gear drive architecture, planetary systems, gear tooth geometry optimization, gears with asymmetric teeth, and gear transmission performance maximization. Dr. Kapelevich is the author of the book titled "Direct Gear Design" and many technical articles. He is a member of the American Gear Manufacturers Association.

Subject Categories

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