Lesson 7: Gear Theory

Lesson contents:

• Introduction: Fundamentals of Gear Transmission
  • From friction to shape: why teeth
  • Fundamental Law of Gearing
  • The Involute Profile: The Universal Solution
  • Standard Nomenclature and Parameters
  • Line of Action and Contact Ratio
• The Interference Phenomenon
  • The theoretical tooth-number limit (\(Z_{lim}\))
  • Cases according to the number of teeth
  • Tooth Correction (Profile Shift)
  • Mounting Types and Center Distance
  • Geometric Calculation of V-mounting
  • Worked Examples
  • Appendix: Involute Function Table
• Velocity Ratio and Number of Teeth: the Continued-Fraction Method
  • The discretization problem
  • Approximation using continued fractions
  • Practical solutions with tooth-count constraints
  • Advantages of the method
• Gear Typology
  • Geometric diversity according to shaft configuration
  • 1. Parallel shafts: spur and helical gears
  • 2. Intersecting shafts: bevel gears
  • 3. Crossed (skew) shafts, non-intersecting
  • 4. Motion transformation: rotation ↔ translation
• Gear Manufacturing
  • Two philosophies: direct forming vs. kinematic generation
  • Main manufacturing methods
  • Quality control