Rack
A rack is a spur gear with an pitch diameter of infinity.
The sides of the teeth are straight lines making an angle to the line
of centers equal to the pressure angle.
Shigley’s Mechanical Engineering Design
Fig. 13–13
Pressure Angle Φ has the values of 20° or 25 °
14.5 ° has also been used.
Gear profile is constructed from the base circle. Then
additional clearance are given.
Standardized Tooth Systems: AGMA Standard
Common pressure angles f : 20º and 25º
Older pressure angle: 14 ½º
Common face width:
Shigley’s Mechanical Engineering Design
3 5
3 5
p F p
pP
FP P
Gear Sources
Shigley’s Mechanical Engineering Design
• Boston Gear
• Martin Sprocket
• W. M. Berg
• Stock Drive Products
….
Numerous others
Conjugate Action
When surfaces roll/slide
against each other and
produce constant angular
velocity ratio, they are said
to have conjugate action.
Can be accomplished if
instant center of velocity
between the two bodies
remains stationary between
the grounded instant centers.
Shigley’s Mechanical Engineering Design
Fig. 13–6
Fundamental Law of Gearing:
Shigley’s Mechanical Engineering Design
The common normal of the tooth
profiles at all points within the mesh
must always pass through a fixed point
on the line of the centers called pitch
point. Then the gearset’s velocity ratio
will be constant through the mesh and
be equal to the ratio of the gear radii.
Conjugate Action: Fundamental Law of Gearing
Forces are transmitted on line
of action which is normal to the
contacting surfaces.
Velocity. VP of both gears is the
same at point P, the pitch point
Angular velocity ratio is
inversely proportional to the
radii to point P, the pitch point.
Circles drawn through P from
each fixed pivot are pitch
circles, each with a pitch
radius.
Shigley’s Mechanical Engineering Design
Fig. 13–6
VP
Gear Ratio
𝑉𝑃 = 𝜔1𝑟1=𝜔2𝑟2
𝜔1
𝜔2=
𝑟2
𝑟1 =
𝑁2
𝑁1
Gear Ratio >1
VP of both gears is the same at point P, the pitch (circle contact) point
ω1
ω2
r2
r1
P
N2 N1
ω2 rotates opposite of ω1
Pitch Circle of Gears
Nomenclature
Smaller Gear is Pinion and Larger one is the gear
In most application the pinion is the driver, This reduces speed
but it increases torque.
Simple Gear Trains
For a pinion 2 driving a gear 3, the speed of the driven gear is
Shigley’s Mechanical Engineering Design
n2 =ω2
n3 =ω3
r3
r2
P
N3 N2
VP
Compound Gear Train
A practical limit on train value for one pair of gears is 10 to 1
To obtain more, compound two gears onto the same shaft
Shigley’s Mechanical Engineering Design
Fig. 13–28