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OutlineGear TheoryNomenclatureGear Trains

Fundamental Law of GearingFunctionally, a gearset is a device to exchange torque for velocity

P=Tωthe angular velocity ratio of the gears of a gearset must remain constant throughout

the mesh

in

out

in

outV r

rm ==ωω

Towards the Involute ProfileA belt connecting the two cylinders

line of action, pressure angle φ

The Involute Profile

Meshing

pressure angle, line of action, length of action, addendum

Nomenclature

Figure 11-8

Ndpcπ

=

2

Pitches, Etc.

circular pitch (mm, in.)

base pitch (mm, in.)

diametral pitch (teeth/in.)

module (mm/teeth)

Ndpc

π=

φcoscb pp =

dNpd =

Ndm =

Velocity Ratiopitches must be equal for mating gears, therefore

in

out

in

outV N

Nrrm ±=±=

Contact Ratio

average number of teeth in contact at any one time =

length of action divided by the base pitch, or,

φπ cosZpm d

p =

( ) ( ) ( ) ( ) φφφ sincoscos 2222 CrarrarZ gggppp −−++−+=

where C=center distance=(Ng+Np)*1/pd*1/2

Minimum # of Teethminimum # of teeth to avoid undercutting with gear and rack

φ2min sin2

=N

OutlineGear TheoryNomenclatureGear Trains

Simple Gear Trains

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Simple Gear Train

R

B

R

P

P

Bv N

NNN

NNm =⎟⎟

⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

Velocity Ratio

R

B

R

G

G

P

P

Black

Black

Y

Y

Bv N

NNN

NN

NN

NN

NNm −=⎟⎟

⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

Simple Gear TrainFine for transmitting torque between

shafts in close proximitywhen mv does not need to be too large

Use third gear (“idler”) only for directional reasons (not for gear reduction)

Reverse on a Car

Actual Manual Transmission For More OnlineAGMAHow Stuff Works Gears