The Geometry of Involute Gears

1 Spur Gears.- 1. The Law of Gearing.- The Requirement for a Constant Angular Velocity Ratio.- Rack and Pinion.- Law of Gearing for Two Gears.- Conjugate Profiles and the Basic Rack.- 2. Tooth Profile of an Involute Gear.- Basic Involute Rack.- Standard Pitch Circle.- The Involute Tooth Profile.- The Involute Function.- Pressure Angle of a Gear.- Tooth Thickness.- Specifying a Spur Gear.- 3. Gears in Mesh.- A Pinion Meshed With a Rack.- A Pair of Gears in Mesh.- Imaginary Rack.- Fundamental Circles of a Gear.- Advantages of the Involute Profile.- 4. Contact Ratio Interference and Backlash.- Contact Ratio.- Interference.- Backlash.- 5. Gear Cutting I Spur Gears.- Form Cutting.- Shaping with a Pinion Cutter.- Advantages of Generating Cutting.- Shaping with a Rack Cutter.- Hobbing.- Cutter Tooth Tip Geometry.- Undercutting.- 6. Profile Shift.- Definition of Profile Shift.- Geometric Design of a Spur Gear Pair.- Alternative Names for Profile Shift.- 7. Miscellaneous Circles.- Highest and Lowest Points of Single-Tooth Contact.- Form Diameter.- Undercut Circle.- 8. Measurement of Tooth Thickness.- Gear-Tooth Vernier Caliper.- Span Measurement.- Measurement Over Pins.- 9. Geometry of Non-Involute Gears.- General Theory.- Fillet Shape Cut by a Rack Cutter.- Fillet Shape of an Undercut Gear.- Profile Modification.- Fillet Shape Cut by a Pinion Cutter.- 10. Curvature of Tooth Profiles.- Involute Radius of Curvature.- Euler-Savary Equation.- Gear Tooth Fillet Radius of Curvature.- 11. Tooth Stresses in Spur Gears.- Contact Force Intensity.- Contact Stress.- Fillet Stress.- 12. Internal Gears.- Tooth Profile of an Internal Gear.- Meshing Geometry of an Internal Gear Pair.- Tip Interference.- Axial and Radial Assembly.- Cutting Internal Gears.- Shape of the Fillet.- Undercutting.- Rubbing.- Geometric Design of an Internal Gear Pair.- Measurement of Tooth Thickness.- 2 Helical Gears.- 13. Tooth Surface of a Helical Involute Gear.- The Basic Helical Rack.- Standard Pitch Cylinder of a Helical Gear.- The Helix and the Involute Helicoid.- The Generator Through Point A.- Direction of the Normal to the Tooth Surface at A.- Tooth Thickness.- Span Measurement.- Tooth Profile in the Normal Section.- Specifying a Helical Gear.- 14. Helical Gears in Mesh.- A Pinion Meshed With a Rack.- A Pair of Helical Gears in Mesh.- Contact Ratio.- Backlash.- Position and Orientation of the Contact Line.- 15. Crossed Helical Gears.- Rack and Pinion.- A Crossed Helical Gear Pair.- Path of Contact.- Contact Ratio.- Backlash.- Tooth Contact Force and Bearing Reactions.- 16. Gear Cutting II Helical Gears.- Shaping with a Pinion Cutter.- Shaping with a Rack Cutter.- Hobbing.- Hobbing Machine Gear Train Layout.- Use of a Differential in the Hobbing Machine.- Theoretically Correct Shape for the Hob Thread.- Geometric Design of a Helical Gear Pair.- 17. Tooth Stresses in Helical Gears.- Tooth Contact Force.- Contact Length.- Contact Stress.- Fillet Stress, and the Equivalent Spur Gear.