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What you will learn:
Simple machines
Mechanical advantage / force ratio
Movement ratio / velocity ratio
Machine efficiency
Gears: gear box ratio, gear efficiency
Directions of rotations
• Is a device that can change magnitude or line of action, or
both magnitude and line of action of a force.
• A simple machine usually amplifies an input force, call the
effort , to give a larger output force, called the load.
• Examples; pulley systems, screw jacks, gear systems
and lever systems.
• A machine is a device that receives energy in
some available form and converts it to a useable
• For example, a person may wish to lift a weight of
2 tonnes; this is not possible unaided but the use
of a jack or a hoist permits the person to achieve
their objective. A lever such as a pry bar is an
example of a simple machine. A relatively small
manual force can be converted into a large force
in order to lift or move an object.
• Leverage and the use of levers occurs in the
use of tools such as spanners, pry bars, pliers
etc., and in many vehicle mechanisms such as
clutch and brake pedals, throttle linkages and
suspension units.
Mechanical advantage
• The mechanical advantage of a machine is the
ratio of the load to the effort:
mechanical advantage, MA = load
• Lifting machines such as jacks and cranes have a
large mechanical advantage so that relatively small
manual forces can be used to raise heavy weights.
Velocity ratio (movement ratio)
• The velocity ratio, VR, of a machine, or
movement ratio, MR, is the ratio of the
distance moved by the effort to the distance
moved by the load:
movement ratio, MR = distance moved by effort
distance moved by load
Efficiency of a machine
• The efficiency of a machine = (energy
output/energy input) in the same time and
this also
Efficiency of machine = MA ×100%
Example problem
• In the trolley jack example shown before an
effort of 250 newtons is lifting a load of 2
tonnes. In lifting the load through a distance
of 15 cm the operator performs 40 pumping
strokes of the handle each of which is 50 cm
long. Calculate the mechanical advantage,
velocity ratio and efficiency of the jack.
• MA = 785
• MR =1333
• The efficiency = 59%
• Leverage and gears
The gear ratio = revolutions of input gear
revolutions of output gear.
• The gear ratio in this case is 4:1
• Gear trains
• Ratio of gear set
= driven × driven
driver driver
= 35×28 = 1225
Problem 1
A simple machine raises a load of 160 kg
through a distance of 1.6m. The effort applied
to the machine is 200N and moves through a
distance of 16m. Taking g as 9.8m/s2,
determine the force ratio, movement ratio
and efficiency of the machine.
Solution 1
• Force ratio = Load/effort
= 160kg/200N
= (160 x 9.8)N/200N
= 7.84
• Movement ratio = distance moved by effort/distance
moved by the load
= 16m/1.6m
= 10
• Efficiency = (force ratio/movement ratio) x 100%
= (7.84/10) x 100
= 78.4%
Problem 2
For the simple machine of Problem 1,
determine: (a) the distance moved by the
effort to move the load through a distance of
0.9m, (b) the effort which would be required
to raise a load of 200kg, assuming the same
efficiency, (c) the efficiency if, due to
lubrication, the effort to raise the 160kg load
is reduced to 180N.
Solution 2
• Distance moved by the effort
= 10 x distance moved by the load
= 10 x 0.9
= 9m
• Since the force ratio is 7.84
effort = load/7.84
= (200 x 9.8) / 7.84
= 250N
Solution 2
• The new force ratio
load/effort = (160 x 9.8)/180
= 8.711
• The new efficiency after lubrication
= (8.711/10) x 100
= 87.11%
Problem 3
•A driver gear on a shaft of a motor has 35 teeth
and meshes with a follower having 98 teeth. If
the speed of the motor is 1400 revolutions per
minute, find the speed of rotation of the
Solution 3
Speed of driver
speed of follower
teeth on follower
teeth on driver
1400/speed of follower = 98/35
Speed of follower = (1400 x 35)/98
= 500 rev/min
Problem 4
•A compound gear train similar to that shown in
last figure consists of a driver gear A, having 40
teeth, engaging with gear B, having 160 teeth.
Attached to the same shaft as B, gear C has 48
teeth and meshes with gear D on the output
shaft, having 96 teeth. Determine;
(a) the movement ratio of this gear system
(b) the efficiency ratio when the force ratio is 6
Solution 4
(a) The speed of D = speed of A x TA/TB x TC/TD
movement ratio = NA/ND = TB/TA x TD/TC
= 160/40 x 96/48
(b) The efficiency = (force ratio/movement ratio)100%
= 6/8 x 100
= 75%