Lecture 2Mechanisms & Machines

The Six Simple Machines

Lever Wheel andAxle Pulley

The Six Simple MachinesInclined Plane ScrewWedge

Simple machines:Gears

Why does a wind turbine need a

gearbox?

By the way…• Where is the safety harness• No fall protection• No eye or hearing protection• This subcontractor would be

removed from the site & possibly terminated

This person has a fun job

The gearboxes are big and they weigh a lot

Gears, Pulleys, & SprocketsThese three power train elements transfer energy through rotary motion.

• Change the speed of rotation• Change the direction of rotation• Change 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

Gears

Mated gears always turn in opposite directions.An Idler Gear allows the driver and driven gears to rotate in the same direction.Mated gears always have the same size teeth (diametric pitch).

GearsThe 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 RatiosVariables to know

n = number of teethd = diameter

ω = angular velocity (speed)τ = torque

** Subscripts in and out are used to distinguish between gears **

4”

nin=din =ωin =τin =

62in.40rpm40 ft-lb

nout =dout =ωout =τout =

124in.20rpm80 ft-lb

Gear Ratios

out out outin

in in out in

n dGR1 n d

τω= = = =

ω τ

Equations to knowGR = Gear Ratio of the gear set

lbftlbft

−−

4080

rpmrpm

2040

.2

.4inin

6122

1

Gear Ratios

= =out

in

nGR1 n

What is the gear ratio between gear A and B?

=5 .42

12 1What 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

Input gear

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!

Compound Gear Trains

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

Here, the two middle gears are connected to a common axle and rotate together

50 T40 T

20 T 10 T

40 410 1

=

AB

C

D

What is the gear ratio between gear A and B?

50 2.520 1

=

What is the gear ratio between gear C and D?

What is the gear ratio of the entire gear train?4 2.5 101 1 1

• =

1= =out

in

GR nn

1= =out

in

GR nn

out out outin

in in out in

n dGR1 n d

τω= = = =

ω τ

Pulley and Belt Systems

out outin

in out in

dd

τω= =

ω τ

.2

.6inin

rpmrpm

1030

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

out

lbft

lbft

−

−

3118

55

What is the purpose/effect of each of these pulleys below?

Do you see something wrong with this pulley/belt arrangement below?

Sprocket and Chain Systems

out out outin

in in out in

n dn d

τω= = =

ω τ

1122

.5.1.3

inin

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

3in.

out1.5in.in

rpmrpm

4590

lbftlbft

−−

60120