ME321 Kinematics and Dynamics of Machines

04/22/23

ME321 Kinematics and Dynamics of

MachinesSteve Lambert

Mechanical Engineering, U of Waterloo

04/22/23

Gears

Spur Gears - Parallel shafts and ‘straight’ teeth

04/22/23

Gears

Example internal spur gear

Example rack and pinion

04/22/23

Helical Gears

Helical gears are smoother and quieter than spur gears, but

are more expensive, are not easily engaged, and they generate a thrust load

04/22/23

Bevel Gears

Straight bevel gears

Skew bevel gears

04/22/23

Hypoid and Worm Gears

Hypoid gear

Worm gear

04/22/23

Fundamental Law of Gearing

We require a constant velocity ratio.

For this to be possible, the common normal of the contacting tooth flanks must always pass through the pitch point.

04/22/23

Involute Action

Imagine that the gears are replaced by two cylinders connected by a string

This system will satisfy our fundamental law

The path traced by Q will represent our tooth profile

04/22/23

Involute Action

These are equivalent.

Path traced by point Q is an Involute.

04/22/23

Gear Tooth Nomenclature

04/22/23

Gear Nomenclature

Pitch CircleCircular PitchAddendumDedendumClearance

Diametral Pitch:

DNP

Circular Pitch:

PNDCP

04/22/23

Standard Gears

DNP

Diametral Pitch:

04/22/23

Interacting Gears

• Centre Distance (r2 + r3)

• Contact Ratio

• Interference

04/22/23

Contact Ratio

Contact ratio is the average number of teeth in contact

CR = length of line of action / base (circle) pitch

CR = l / BP

04/22/23

Contact Ratio

CR = l / BP, where:

Line of action:

l = AC-AP + DB-DP

NrBP

rDP

rarDB

rAPrarAC

B

2sin

cos

sincos

3

23

233

2

22

222

04/22/23

Interference

Interference occurs if point C falls outside point D

- contact beyond involute profile occurs if

O2C > O2D

where:

2222

222

sincrDO

arCO

b