design of levers

Design of Levers

LEVER• A lever includes a stiff structure that rotates

around a fixed point called the fulcrum.

• A lever is defined as a mechanical device in the

form of a rigid bar pivoted about the fulcrum to

multiply or transfer the force.

fulcrum

Anatomy of the lever

• Fulcrum – point around which the lever rotates

• Input Force – Force exerted ON the lever

• Output Force – Force exerted BY the lever

Lever

The construction of a simple lever is shown in Fig.

F is the force produced by the lever and P is the effort

required to produce that force. The force F is often called

'load'. The perpendicular distance of the line of action of

any force from the fulcrum is called the arm of the lever.

Therefore l1 and l2 are effort arm and load arm respectively.

Lever

Taking moment of forces about the fulcrum,

F x l2 = P x l1

or

F/P = l1/l2

The ratio of load to effort i.e. (F/P) is called the 'mechanical

advantage' of fever. The ratio of the effort arm to the load

arm i.e. (I1/l2) is called the 'leverage'. Therefore,

mechanical advantage is equal to the leverage.

Lever

F x l2=P x l1

or

F/P= l1/l2

It is seen by Eq., that a large force can be exerted by a

small effort by increasing leverage, i.e. increasing l1and reducing l2 .

In many applications, it is not possible to increase

effort arm l1 due to space restrictions.In such

applications, compound levers are used to obtain more

leverage.

Three Classes of LeversThere are three types of lever, based on the relative positions

of the effort point, the load point and the fulcrum

They are as follows:

First Class - fulcrum between Input and output-

This type of lever is used in applications like the rocker arm for the

overhead valves of internal combustion engine, bell crank levers in

railway signal mechanism and levers of hand pump

Second Class – output between fulcrum and input-

This type of lever is used in lever loaded safety valve mounted on

the boilers.

Third Class – input between fulcrum and output- This type

of lever is not recommended in engineering applications. A picking

fork

Design of Levers

Lever design consists of two aspects

1) Length of lever- which is decided on the basis of

leverage required to exert a given load F by means

of an effort P

2) The cross-section of the lever is designed on the

basis of bending stresses.

3) Fulcrum pin diameter

Design of Levers

Steps for Design of Lever

1) Force analysis:

In any application, the load or the force F, to be

exerted by the lever is input.

The effort required to produce this force is

calculated by taking moments about the

fulcrum. Therefore,

F x l2=P x l1

P=F x l2 / l1


The free body diagram of forces acting on the 'first'

type of the lever is shown in Fig. R is the reaction at

the fulcrum pin. Since the sum of vertical forces acting

on the lever must be equal to zero,

R = F + P

Free Body Diagram of Forces Acting on First Type of Lever


The free body diagram of forces acting on the 'second'

type of the lever is shown in Fig. In this case, the load

and the effort act in opposite direction. Considering

equilibrium of forces in vertical direction,

F = R + P

Free Body Diagram of Forces Acting on SecondType of Lever

R = F - P

Steps for Design of LeverIn above two cases, the forces are assumed to be

parallel. Sometimes, the forces F and P act along lines

that are inclined to one another as shown in Fig.

In such cases, l1 is perpendicular distance from the

fulcrum to the line of action of force P.

Similarly l2 is perpendicular distance from the fulcrum

to the line of action of force F


The magnitude of reaction R is equal to the resultant of

load F and effort P. It can be determined by parallelogram

law of forces. (ii) The line of action of reaction R passes

through the intersection of F and P i.e. point o & fulcrum


Figure illustrates a bell crank lever with the arms, that are

inclined at angle θ with one another. The load F and the

effort P act at right angles to their respective arms. The

reaction R at the fulcrum is given by

Design of Lever Arm

When the forces acting on the lever are determined,

the next step in lever design is to find out the

dimensions of the cross-section of the lever.

The cross-section of the lever is subjected to bending

moment. In case of two arm lever, as shown in Fig., the

bending moment is zero at the point of application of P

or F and maximum at the boss of the lever.

Design of Lever Arm

The cross-section at which the bending moment is

maximum can be determined by constructing bending

moment diagram. In Fig., the bending moment is

maximum at section XX and it is given by,

Design of Lever ArmThe cross- section of the lever can be rectangular,

elliptical or I-section. For rectangular cross-section,

For elliptical cross-section,

where a and b are major and minor axes of the section. Usually, major axis istaken as twice of minor axis.

Using the above mentioned proportions, the

dimensions of the cross-section of the lever can be

determined by,

Design of Fulcrum PinThe fulcrum pin is subjected to reaction R as shown in

Fig. The forces acting on the boss of lever and the pin are

equal and opposite.

The dimensions of the pin, viz. diameter dp and length lp in

lever boss are determined by bearing consideration and

then checked for shear consideration.

There is relative motion between the pin and the lever and

bearing pressure becomes the design criterion. The

projected area of the pin is (dp x lp). Therefore,

Design of Fulcrum PinFor the fulcrum pin, the ratio of length to diameter (lp /dp)

is usually taken between 1 to 2. The outside diameter of

boss in the lever is taken as twice of the diameter of pin

i.e. (2 x dp). A phosphor bronze bush, usually 3mm thick is

fitted inside the boss to reduce the friction.

The permissible bearing pressure for phosphor bronze

bush is 5 to 10 N/mm . Lubricant is provided between the

pin and the bush to reduce the friction.

design of levers

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