THOERY OF MECHANISMS AND

MACHINES

Gears

Prepared by:

Abhishek AttalFinal Year Dual Degree Student

Department of Mechanical EngineeringIndian Institute of Technology Kanpur

attalab@iitk.ac.in NL-312

Gears (Higher Pair)

• Type of Gears

• Nomenclature

• Involute Profile

• Gear Construction

• Gear Trains

• Questions and examples

Types of GearsAccording to the position of axes of the shafts

• ParallelSpurHelicalRack and Pinion

• IntersectingBevel Gear

• Non intersectingWorm and worm wheel

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)

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

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

= diameter of pitch circle

= Number of teeth

• 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

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

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)

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.

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

QuestionThe 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 contact2) Contact ratio if the number of teeth on the larger gear is 20

Primary Gear Characteristics

• Pressure angle/ tooth profile

• Face Width

• Gear ratio or number of teeth on both gears

• Centre to centre distance

• Module

Thank You