1. THOERY OF MECHANISMS AND MACHINES
Module-09
Gears
Instructed by:
Anupam Saxena
Associate Professor
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
FB 361
Prepared by:
Abhishek Attal, Abhishek Sharma
Final Year Dual Degree Student
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
NL-312, FB369

2. Gears (Higher Pair) Type of Gears Nomenclature Gear Construction
Involute Profile
Gear Trains
Examples, problems and questions

3. According to the position of axes of the shafts
Types of Gears
According to the position of axes of the shafts
Parallel
Spur
Helical
Rack and Pinion
Intersecting
Bevel Gear
Non intersecting
Worm and worm wheel

4. Spur Gears Used in transmitting torque between parallel shafts
Simplest type
Teeth are cut parallel to shaft axis
Easy to manufacture
If one of the gears has infinite diameter,
Rack and pinion arrangement

5. Helical Gear Used in transmitting torque between parallel shafts
Teeth are cut at an angle with the shaft axis
Helical gears can be meshed in parallel or crossed orientations. 
The angled teeth engage more gradually than spur gear teeth,
causing them to run more smoothly and quietly
Double Helical gear

6. Bevel Gears Used to transmit rotary motion between intersecting shafts
Tooth-bearing faces of the gears are conically shaped
Bevel gears are most often mounted on shafts that are
90 degrees apart, but can be designed to work at other
angles as well.
The pitch surface of bevel gears is a cone

7. Worm and Worm Gear Used for high Gear ratios
Direction of transmission (input shaft vs output shaft)
is not reversible when using large reduction ratios
Used in wiper motors

8. Fundamental Law of Gearing
The condition to maintain a constant angular velocity ratio between two gears is that the common normal at the point of contact should meet the line joining the centers at a fixed point.

9. Terminology (Spur?) Pinion and wheel: small – pinion, large – wheel
Pitch Curve: theoretical curve along which gear rolls (without slipping)
Circular Pitch: distance measured along
the pitch circle from one point of tooth to
the corresponding point in adjacent tooth
Diametral Pitch: no. of teeth per unit
length of the PCD
Module: inverse of Diametral pitch
Addendum: radial distance b/w PC and top
land
Dedendum: radial distance b/w PC and bottom land
Clearance: amount by which dedendum of gear
exceeds the addendum of the mating gear

10. Equations
𝑝= 𝜋 𝑑 𝑝 𝑁
𝑃= 𝑁 𝑑 𝑝
𝑚= 𝑑 𝑝 𝑁
𝑎=𝑚
𝑏=1.25×𝑚
𝜔 1 𝜔 2 = 𝑁 1 𝑁 2

11. Involute Profile Curve traced by a point on a string unwrapping
from a cylinder is involute profile

12. Pressure Angle Common normal to the mating tooth curves at
the point of contact makes a constant angle with
the common tangent to the pitch circles passing
through the pitch point. This angle is called
pressure angle.

13. Primary Gear Characteristics
Pressure angle/ tooth profile
Face Width
Gear ratio or number of teeth on both gears
Centre to centre distance
Module

14. Construction