Islamic University of Gaza
Faculty of Engineering
Mechanical Engineering Department
Whitworth Quick Return Mechanism
: Prepared By
Mahmoud Abdullhadi Badran 120141989
Monther Hatem Al-Saafin 120141046
Ahmed Yehia AL-agha 120140849
: Submitted to
Dr. Mohammad Abuhaiba
Eng. Ibrahim Al-Baik
Due. December 19th 2016
Table of Contents
Page
Objectives. 1-1
Introduction..1-9-2
Results and-3
Discussion.10
Conclusion11-4
Recommendations11-5
References11-6
Appendiceses11-7
I
List of Figures
Figure page
. Fig (1) : Whitworth Quick Return Mechanism 2
Fig (2) : Schematic Diagram for Whitwprth Quick 4
. Return Mechanism
. Figure (3) : Balancing of sloting Bar 8
.Figure (4) : results 9
. Figure(5) : Balancing of crank 9
List of Tables
Table Page
.Table (1) : Data Of Sloting Bar 8
II
Abstract
In this project we study Whitworth Quick Return Mechanism and make
Kinematic Complex Number analysis (Position , Velocity , Acceleration and
Force analysis ) for the mechanism we have , and also make balancing for
Rotating and Reciprocating parts ,after that use Matlab for programming
data and draw curves that represent the behavior of the mechanism , also
use Solidworks and Adams to make simulation for the mechanism parts , and
. compare between results of each software
III
: Objectives-1
To determine the kinematics quantities such as Displacement, Velocity and -1
. Acceleration of the elements of the mechanism
. To determine different forces acted on the mechanism-2
To establish the relationship between the motions of various parts of the -3
. mechanism
. To compare between the predicted results and results on graphs -4
.To identify the function of each part of the machine-5
: Introduction-2
: Literature Review 2.1
The whitworth quick return mechanism converts rotary motion into *
. reciprocating motion
The forward reciprocating motion is slower rate than the return stroke, this *
. why it is called quick return mechanism
This mechanism is made of a driving crank and of a driven slider crank , in *
the considered configuration the fixed pivot of the driven crank located at
. point C
. This mechanism is mostly used in shaping and slotting machines *
In this mechanism, the link CD (link 2) forming the turning pair is fixed, as *
. showing in the fig
. The link 2 corresponds to a crank in a reciprocating steam engine *
. The driving crank (link 3) rotates at a uniform angular speed *
The slider (link 4) attached to the crank pin at A slides along the slotted bar *
. PA (link 1) which oscillates at a pivoted point D
. The connecting rod PR carries the arm at R to which a cutting tool is fixed *
The motion of the tool is constrained along the line RD produced , i.e. along *
. a line passing through D and perpendicular to CD
When the driving crank CA moves from the position CA1 to CA2 (or the link *
DP from the position DP1 to DP2) through an angle in the clockwise direction,
the tool moves from the left hand end of its stroke to the right hand end
.through a distance 2PD
Now when the driving crank moves from the position CA2 to CA1 (or the *
link DP from DP2 to DP1 ) through an angle in the clockwise direction, the
.tool moves back from right hand end of its stroke to the left hand end
A little consideration will show that the time taken during the left to right *
movement of the ram (i.e. during forward or cutting stroke) will be equal to
.the time taken by the driving crank to move from CA1 to CA2
Similarly, the time taken during the right to left movement of the ram (or *
during the idle or return stroke) will be equal to the time taken by the driving
.crank to move from CA2 to CA1
Since the crank link CA rotates at uniform angular velocity therefore time *
taken during the cutting stroke (or forward stroke) is more than the time
.taken during the return stroke
In other words, the mean speed of the ram during cutting stroke is less *
. than the mean speed during the return stroke
. Fig (1) : Whitworth Quick Return Mechanism
: Why this project 2.2
Whitworth Quick Return Mechanism is a complicated project , we
choose it to challenge ourselves whether we are able to do a
. complex project like this , we hope that our purpose is done
: Theory 2.3
There are three main equations used in complex number
: analysis
i
Equation (2.3.1) r=r x +ir y =r ( cos+i sin )=r e
dr
Equation (2.3.2) =r =( r +i rw ) e i
dt
d r 2 i
Equation (2.3.3) =r =( r + i 2 r w+i rr w )e
dt
: Design 2.4
. Fig (2) : Schematic Diagram for Whitwprth Quick Return Mechanism
: Given
3= 4
r6 , r5 , r4 , r2 , r1
6 , 4 , 3 , 1=90
: Variable
r7 , r3
5 , 2
4
: Kinematic Analysis 2.5
Equation (2.5.1) . r 1 +r 3=r 2
Equation (2.5.2) . r 1 +r 4 +r 5=r 6 +r 7
: Position Analysis 2.5.1
: using Equation (2.3.1) and Equation (2.5.1) we have
2
r 3= ( r 2 cos 2 ) + ( r 2 sin 2r 1 )
2
r 2 sin 2r 1 sin 1
3=tan1 ( r 2 cos 2r 1 cos 1 )
: using Equation (2.3.1) and Equation (2.5.2) we have
r 4 cos 4 +r cos + r 5 cos 5
r 7= cos 7 > 0
cos 7
r 4 sin 4 +r sin +r 5 sin 5
r 7= when cos 7=0(not necessary)
sin 7
5= 7sin 1 ( r 6 sin ( 7 6 )r 1 sin ( 7 1 )r 4 sin ( 7 4 )
r5 )
: Velocity Analysis 2.5.2
: using Equation (2.3.2) and Equation (2.5.1) we have
r 2 sin 2 2+r 3 sin 3 3
r 3=
cos 3
r 2 cos 2 2 +r 3 cos 3 3
r 3=
sin 3
r 2 2 [ sin 2 sin 3 +cos 2 cos 3 ]
3 =
r3
r 4 cos 4 4
5 =
r 5 cos 5
: Acceleration Analysis 2.5.3
6
Balancing 2.6
7
Sloting Bar
Figure (3) : Balancing of sloting Bar
Balancing of a Single Rotating Mass By Two Masses
Rotating
Table (1) : Data Of Sloting Bar
Couple 2 Distance Cent. force Radius Mass Plane
2
0 0 m* r4 r4(input) m A
m1* r1*l1 l1 m1* r1 r1 m1 B
m2 *r2*l2 l2 m2 *r2 r2 m2 C
8
Figure (4) : results
Fc=m 2r
2
Fc 1=m 1 r 1
Fc 2=m 2 2r 2
mr =m1r 1+ m2r 2
: Crank
Figure(5) : Balancing of crank
m1l1=m2l2
9
: Results and Discussion-3
10
: Conclusion -4
After making Kinematic analysis for the mechanism , we recognize that the
diagrams that we have from Adams come up with the predicted results from
. Kinematic analysis
: Recommendations-5
We use matlab program to make different diagrams of Kinematic properties
for the mechanism and we note that the results are illogical , after that we
. resort to Adams and we find that the results are logical
: References -6
. Dynamic Book *
. Mechanism and Machine theory Book *
. Theory of machine Book *
: Appendiceses-7
. Displacement Analysis sheet *
. Velocity Analysis sheet *
. Acceleration Analysis sheet *
. Force Analysis sheet *
11
