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

chapter 2|32 pages

Macrogeometry of Asymmetric Tooth Gears

chapter 3|34 pages

Area of Existence

chapter 4|16 pages

Asymmetric Gearing Limits

chapter 5|50 pages

Gear Geometry Optimization

chapter 7|18 pages

Special Types of Asymmetric Gears

chapter 8|16 pages

Tolerancing and Tolerance Analysis

chapter 9|22 pages

Asymmetric Gear Manufacturing

chapter 10|11 pages

Symmetric vs. Asymmetric Gears

chapter 11|22 pages

Asymmetric Gear Applications