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

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

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

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

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

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

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

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.

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

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

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

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.

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

Construction