Mechanical Engineering Principles

18

Simple machines

At the end of this chapter you should be

able to:

• define a simple machine


• define force ratio, movement ratio, effi-
  ciency and limiting efficiency


• understand and perform calculations with
  pulley systems


• understand and perform calculations with
  a simple screw-jack


• understand and perform calculations with
  gear trains


• understand and perform calculations with
  levers

18.1 Machines

A machine is a device that can change the magni-
tude or line of action, or both magnitude and line of
action of a force. A simple machine usually ampli-
fies an input force, called theeffort,togivealarger
output force, called theload. Some typical examples
of simple machines include pulley systems, screw-
jacks, gear systems and lever systems.

18.2 Force ratio, movement ratio and

efficiency

Theforce ratioormechanical advantageis defined
as the ratio of load to effort, i.e.

Force ratio=

load

effort

( 18. 1 )

Since both load and effort are measured in newtons,
force ratio is a ratio of the same units and thus is a
dimension-less quantity.

Themovement ratioorvelocity ratiois defined

as the ratio of the distance moved by the effort to

the distance moved by the load, i.e.

Movement ratio=

distance moved

by the effort

distance moved

by the load

( 18. 2 )

Since the numerator and denominator are both mea-

sured in metres, movement ratio is a ratio of the

same units and thus is a dimension-less quantity.

Theefficiency of a simple machineis defined as

the ratio of the force ratio to the movement ratio,

i.e.

Efficiency=

force ratio

movement ratio

=

mechanical advantage

velocity ratio

Since the numerator and denominator are both

dimension-less quantities, efficiency is a dimension-

less quantity. It is usually expressed as a percent-

age, thus:

Efficiency=

force ratio

movement ratio

×100% ( 18. 3 )

Due to the effects of friction and inertia associated

with the movement of any object, some of the input

energy to a machine is converted into heat and

losses occur. Since losses occur, the energy output

of a machine is less than the energy input, thus the

mechanical efficiency of any machine cannot reach

100%

For simple machines, the relationship between

effort and load is of the form:Fe=aFl+b,where

Fe is the effort,Fl is the load andaandb are

constants.

From equation (18.1),

force ratio =

load

effort

=

Fl

Fe

=

Fl

aFl+b