Gears, Pulley Drives, and Sprockets

Nanotechnology Simple Machines

Gears, Pulleys, & Sprockets

These three power train elements transfer energy through rotary motion.

Change the speed of rotationChange the direction of rotationChange the amount of torque available to do work

Gears

A gear train is made when two or more gears are meshed

A gear train is a mechanism used for transmitting rotary motion and torque through interlocking teeth.

Driver gear causes motion

Motion is transferred to the driven gear

GearsMating gears always turn in opposite directions.

An Idler Gear allows the driver and driven gears to rotate in the same direction.

Mating gears always have the same size teeth (diametric pitch).

Gears

The rpm of the larger gear is always slower than the rpm of the smaller gear.

Gears locked together on the same shaft will always turn in the same direction and at the same rpm.

Gear Ratios

Variables to know

n = number of teeth

d = diameter

w = angular velocity (speed)

t = torque ** Subscripts in and out are used to distinguish between gears **

4”

nin=

din =

win =

tin =

6

2in.

40rpm

40 ft-lb

nout =

dout =

wout =

tout =

12

4in.

20rpm

80 ft-lb

Gear Ratios

out out outin

in in out in

n dGR1 n d

Equations to knowGR = Gear Ratio

lbft

lbft

40

80

rpm

rpm

20

40

.2

.4

in

in

6

12

1

?

2

1

Gear Ratios

out

in

nGR1 n

What is the gear ratio between gear A and B?

5 .4212 1

What is the gear ratio between gear B and C?

20 45 1

What is the gear ratio between gear C and D?

12 .620 1

out

in

nGR1 n

out

in

nGR1 n

Gear Ratios

0.6 0.42 41 1 1

What is the TOTAL gear train gear ratio?

What would the total gear ratio be if the last gear had 40 teeth?

0.6 0.42 8 21 1 1 1

11

If gear A and D were directly connected to each other, what would the resulting gear ratio be?

20 120 1

or out

in

nGR 40 21 n 20 1

out

in

nGR1 n

Idler gears don’t affect GR!

Example Compound Machine• Here are 3 mechanisms in series:• #1 Wheel-axle• #2 Gear train• #3 Wheel-axle

Gear Ratios – Compound Machines

• Used similarly to MA• Applies to torque instead of force

• In a compound machine, total MA and GR are products of components

• MA used only to calculate forces, not torques.• GR used only to calculate torques, not forces.

Example Compound Machine• Mechanism #1: Wheel-axle

Example Compound Machine• Mechanism #2: Gear train

Example Compound Machine• Mechanism #3: Wheel-axle

Example Compound Machine

Example Compound Machine

Compound Gear Train

The two middle gears share a common axle, so they rotate at the same speed.

This allows the final gear to rotate slower and produce more torque than if it were connected only to the driver gear.

Driver

Compound Gear Ratios

50 T40 T

20 T10 T

40 4

10 1

AB

C

D

What is the gear ratio between gear A and B?

50 2.5

20 1

What is the gear ratio between gear C and D?

What is the gear ratio of the entire gear train?4 2.5 10

1 1 1

1 out

in

GR n

n

1 out

in

GR n

n

Pulley and Belt Systems

out outin

in out in

dd

.2

.6

in

in

rpm

rpm

10

30

Equations

d = diameter ω = angular velocity (speed) t = torque

out

in

lbft

lbft

31

18

552i

n.

Sprocket and Chain Systems

out out outin

in in out in

n dn d

11

22.5.1

.3

in

in

n = number of teeth d = diameter ω = angular velocity (speed) τ = torque

3in.

out

1.5in.

in

rpm

rpm

45

90lbft

lbft

60

120

Because both gears use the same chain and have teeth of the same size, you can count the number of teeth to find the IMA, as follows.

• Shifting gears on a bicycle is a way of adjusting the ratio of gear radii to obtain the desired IMA.

• If the pedal of a bicycle is at the top or bottom of its circle, no matter how much downward force you exert, the pedal will not turn.

• On a multi-gear bicycle, the rider can change the MA of the machine by choosing the size of one or both gears.

• When accelerating or climbing a hill, the rider increases the ideal mechanical advantage to increase the force that the wheel exerts on the road.

• To increase the IMA, the rider needs to make the rear gear radius large compared to the front gear radius.

• For the same force exerted by the rider, a larger force is exerted by the wheel on the road. However, the rider must rotate the pedals through more turns for each revolution of the wheel.

• On the other hand, less force is needed to ride the bicycle at high speed on a level road.

• An automobile transmission works in the same way. To accelerate a car from rest, large forces are needed and the transmission increases the IMA.

• At high speeds, however, the transmission reduces the IMA because smaller forces are needed.

• Even though the speedometer shows a high speed, the tachometer indicates the engine’s low angular speed.

Pulley SprocketMethod of

Transmitting Force

Belt Chain

Advantages Quiet, no lubrication needed, inexpensive

No slip, greater strength

Disadvantages Can slipHigher cost, needs lubrication, noisy

Comparing Pulleys and Sprockets

Image ResourcesMicrosoft, Inc. (2008). Clip art. Retrieved January 15, 2008, from http://office.microsoft.com/en-us/clipart/default.aspx