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1-Objective

1 The experiment is designed to give a better

understanding of the performance of the four-

bar linkages and crank slider in its dierent

conditions according to its geometry.

2 To calculate and measure the value theta 3

and theta four for four bar linkage.

3 To calculate and measure the value of theta 3

and length d.

2-Introduction

A slider crank mechanism converts circular motion

of the crank into linear motion of the slider In

order for the crank to rotate fully the condition !"#$% must be satis&ed 'here # is the crank length(

! is the length of the link connecting crank and

slider and % is the oset of slider A slider crank is

a ###) type of mechanism ie It has three revolute

 joints and * prismatic joint The total distance

covered by the slider bet'een its t'o extreme

positions is called the path length.

 +inematic inversion of slier crank mechanisms

produce ordinary a 'hite 'ork ,uick return

mechanism of achines !ab Inversion. /ierent

mechanisms obtained by &xing dierent links of a

kinematics chain are kno'n as its inversions.

Fig. 1,1 

crank slider

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A four-bar linkage( also called a four-bar( is thesimplest movable closed chain linkage It consistsof four bodies( called bars or links( connected in aloop by four joints 0enerally( the joints arecon&gured so the links move in parallel planes( andthe assembly is called a planar four-bar linkage.

If the linkage has four hinged joints 'ith axesangled to intersect in a single point( then the linksmove on concentric spheres and the assembly iscalled a spherical four-bar linkage 1ennett2slinkage is a spatial four-bar linkage 'ith hinged

 joints that have their axes angled in a particular'ay that makes the system movable.

 The term often refers to a human-po'ered crank

'hich is used to manually turn an axle( as in

a bicycle crankset or a brace and bit drill In this

case a person2s arm or leg serves as the

connecting rod( applying reciprocating force to the

crank There is usually a bar perpendicular to the

other end of the arm( often 'ith a freely rotatablehandle or pedal attached.

Fig 1,2 

4-bar

linkage

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3- Theory

 To &nd theta 3 and d for crank slider 'e use this

e,uation:

 ɵ3 = sin-1 ((c-a sin ɵ2 )/b)

 d = a cos ɵ2 – b cos ɵ3

 To &nd theta 3 and theta for four bar linkage 'e

use this e,uation:

k 1=d/a, k 2=d/c , k 3= ((a2 )-(b2 ) + (c2 ) + (d 2 ))/ (2ac) ,

k 4=d/b ,

k 5= ((c2 )-(d 2 )-(a2 )-(b2 ))/ (2ab)

 A=cos (ɵ2 )-k1+k3-k2*cos (ɵ2 )

B=-2*sin (ɵ2 )

C=k 1-k 2*cos (ɵ2 ) +k 3-cos (ɵ2 )

D=cos (ɵ2 )-k 1+k 5+k 4*cos (ɵ2 )

E=-2*sin (ɵ2 )

F=k 1+k 4*cos (ɵ2 ) +k 5-cos (ɵ2 )

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θ3=2∗tan−1(− E±√  E2

−4 df 

2d   )

θ4=2∗arctan

(−B±√ B

2−4  AC 

2  A

  )

4-%,uipment:

14rank slider

 2-5our bar linkage 

5-data:

-5or crank slider:

a6 778 9 b 6 7:8

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θ2

°d   θ3

°d calculated 

0   25 0 20

40   21 7.4 21

90   24.5 11.5 24.5

120   27.2 10 27

160   30 4 29.8

180   31 0 29.7

-5or the four bar linkage:

a6 778 9 b 6 7*; 9 c= 0.2 / d =0.2

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θ2

°θ4

°θ3,1

°θ3,2

°θ4,1

°θ4,2

°

0   52 -111 111 59 -59

60   20 - - -1656 -16

120   45 -254 661 -470 -36

180   55 -310 310 193 -193

240   70 -661 254 36 470

6-conclusion:

In order for the crank to rotate fully the condition

!" #$% must be satis&ed 'here # is the crank

length ! is the length of the link connecting crank

and slider and % is the oset of slider A slider

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crank is a ###) type of mechanism ie It has three

revolute joints and * prismatic joint.