This document discusses different types of gears used in mechanical systems to transmit rotational motion between parallel or intersecting shafts. It describes spur gears, helical gears, bevel gears, and worm gears. Key terminology for gears like pitch circle, diametral pitch, module, addendum, dedendum, and contact ratio are defined. The fundamental law of gearing relating the rotational speeds of meshing gears is explained. Involute tooth profiles and pressure angles are also covered.

1. THOERY OF MECHANISMS
AND MACHINES
Gears
Prepared by:
Abhishek Attal
Final Year Dual Degree Student
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
attalab@iitk.ac.in NL-312

2. Gears (Higher Pair)
• Type of Gears
• Nomenclature
• Involute Profile
• Gear Construction
• Gear Trains
• Questions and examples

3. 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 Gear
• Used in transmitting torque between parallel shafts
• Simplest type of gear
• Teeth are cut parallel to shaft axis
• Easy to manufacture
• If one of the gear has infinite diameter, then
it is called rack, ( Rack and pinion)

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. Terminology
• Small Gear– Pinion
• Large Gear – Wheel
• Pitch Curve: theoretical curve along
which gear rolls (without slipping)
• Circular Pitch (p): distance measured
along the pitch circle from one point of
tooth to the corresponding point in
adjacent tooth
𝑝 =
𝜋𝑑 𝑝
𝑁
𝑑 𝑝= diameter of pitch circle
𝑁= Number of teeth

9. • Diametral Pitch: no. of teeth per unit length of the PCD
𝑃 =
𝑁
𝑑 𝑝
• Module: inverse of Diametral pitch
𝑚 =
𝑑 𝑝
𝑁
• Addendum: radial distance b/w PC and top land
𝑎 = 𝑚
• Dedendum: radial distance b/w PC and bottom land
𝑏 = 1.25 × 𝑚
• Clearance: amount by which dedendum of gear exceeds the addendum of the
mating gear
𝑐 = 𝑏 − 𝑎

10. Fundamental Law of Gearing
• Let, N be the number of teeth from each
gear passing through engagement zone in
1 second
• Number of teeth on two gears 1 and 2 be
N1 and N2 respectively
• Gear 1 and 2 make (N/N1) and N/N2)
revolution
𝜔1 =
2𝜋𝑁
𝑁1
𝜔2 =
2𝜋𝑁
𝑁2
𝜔1
𝜔2
= −
𝑁1
𝑁2

11. 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 (Pitch Point)
𝜔1
𝜔2
=
𝑂2 𝑃
𝑂1 𝑃

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

13. 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.

14. Contact Ratio
• To transmit rotational motion continuous there must be at least one pair of
contacting teeth at all times
• Typically, there are more than one pair in contact, hence overlapping of teeth
• Contact Ratio is used to provide quantitative measure of the amount of overlap
𝐶𝑜𝑛𝑡𝑎𝑐𝑡 𝑅𝑎𝑡𝑖𝑜 𝑚 𝑐 =
𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑐𝑡𝑖𝑜𝑛
𝑏𝑎𝑠𝑒 𝑝𝑖𝑡𝑐ℎ
𝑏𝑎𝑠𝑒 𝑝𝑖𝑡𝑐ℎ(𝑝 𝑏) =
2𝜋𝑟𝑏2
𝑁2

15. 𝑚 𝑐 =
𝐸𝐹
𝑏𝑎𝑠𝑒 𝑝𝑖𝑡𝑐ℎ
=
𝑆𝑇
𝑏𝑎𝑠𝑒 𝑝𝑖𝑡𝑐ℎ
=
𝐸𝐹
𝑝 𝑏
𝐸𝐹 = 𝐸𝐹 + 𝐴𝐸 + 𝐸𝐹 + 𝐵𝐹
− 𝐴𝐸 + 𝐵𝐹 + 𝐸𝐹
𝐸𝐹 = 𝐴𝐹 + 𝐵𝐸 − 𝐴𝐵
𝐴𝐵 = 𝐶𝑠𝑖𝑛𝛼 𝐶 = 𝑟𝑝1
+ 𝑟𝑝2
Contact Ratio

16. Question
The pitch circle radii of two involute spur gears in mesh are 51.5mm
and 64.2mm. The outer circle radii are 57.5mm and 71.2mm,
respectively, the operating pressure angle being 20 degrees. Determine
1) Length of the path of contact
2) Contact ratio if the number of teeth on the larger gear is 20
𝑟𝑏 = 𝑟𝑝 𝑐𝑜𝑠𝛼

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

18. Thank You