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KINEMATICS OF MECHANISMSKINEMATICS OF MECHANISMS(BDC4043)
Lecture Module 3: Analysis of Position and Displacement
Waluyo Adi SiswantoUniversiti Tun Hussein Onn Malaysia
This module is licensed under a Creative Commons Attribution 3.0 License.
http://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/ -
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Lecture Module 3 BDC4043 2
Topics
nderstandin! position and displacementDisplacement"position analysis #!raphical and analytical$Limit position #!raphical and analytical$Complete CyclePosition Dia!ramDisplacement dia!ram
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Lecture Module 3 BDC4043 3
Position and displacementdefinition
PositionPositionrefers to the location of an ob%ect
Position of a point P
O
P
RP
RP RP={RPxRPy}
N
A
An!ular position of a point N(AN ,)
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Lecture Module 3 BDC4043 4
Position and displacementdisplacement
Displacement (Shift)Displacement (Shift)is the end product of movement #motion$.&t is a vector that represents the distance bet'een the startin! and endin! positionof a point or lin(.
O
P
RP
N
A
Linear displacement
P '
RP
'
RP
RP=R
P'R
P
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Lecture Module 3 BDC4043 5
Position and displacementdisplacement
Displacement (Shift)Displacement (Shift)is the end product of movement #motion$.&t is a vector that represents the distance bet'een the startin! and endin! positionof a point or lin(.
O
P
N
A '
an!ular displacement
= '
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Lecture Module 3 BDC4043 6
Displacement analsisdegrees of freedom
De!"ees of f"eedomDe!"ees of f"eedom(mo#ilit)(mo#ilit)is the number of independent inputs re)uired to preciselyposition all lin(s of the mechanism 'ith respect to the !round.
D*+, the number of actuators needed to operate the mechanism.
-rueblers e)uation: F=3(n1)2 jpj h
, total number of lin(s includin! frames
, total number of primary %oints #pins or slidin! %oints$
, total number of hi!her/order %oints #cam or !ear %oints$
n
jp
jh
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Lecture Module 3 BDC4043 7
Displacement analsisdegrees of freedom
F! Constrained mechanism
F" Loc(ed mechanism
F#! nconstrained mechanism
F=3(41)2(4)0
F=3(31)2(3)0
F=1
F=0
F=3(51)2(5)0
F=2
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Lecture Module 3 BDC4043 8
E$ample %&'
&dentify the mobility #dof$ of follo'in! mechanisms:
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Lecture Module 3 BDC4043 9
1
3 2
4
&dentify the lin(s : 4 lin(s
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Lecture Module 3 BDC4043 10
1
3 2
4
&dentify the %oints : 4 pin %oints 5 slidin! %oint
A
6
C
D
7
+ , 3#4/$ 8 1#9$ ,
$ounted as % pin &oints
T'e mec'anism wor(sonly from ! actuator
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Lecture Module 3 BDC4043 11
inematics dia!ram
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Lecture Module 3 BDC4043 12
&dentify the lin(s : 2 lin(s
&dentify the %oints : 3 pin %oints 5 slider %oints
+ , 3#2/$ 8 1#2$ ,
T'e mec'anism wor(sonly from ! actuator
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Lecture Module 3 BDC4043 13
Displacement analsisgrap'ical met'od
;tartin! from the driver #master$ 'here the actuator located2 at Df. The intersection #d$ and #e$ is point C. Dra' lin( 6C!. Dra' lin( CD
6
D
C
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Lecture Module 3 BDC4043 19
A
6
D
C
30o
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Lecture Module 3 BDC4043 20
A
6 D
C
60o
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Lecture Module 3 BDC4043 21
6
D
C
90o
A
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Lecture Module 3 BDC4043 22
A
6
DC
120o
Displacement analsis
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Lecture Module 3 BDC4043 23
Displacement analsisanalytical met'od
020
30o
Determine #analytically$ the displacement of the clamp surface as thehandle rotates do'n'ard de!.
Do the same thin! by usin! a !raphical method.
Displacement analsis
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Lecture Module 3 BDC4043 24
Displacement analsisanalytical met'od
020
30o
A
6
C
020
30o
;implified model
Displacement analsis
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Lecture Module 3 BDC4043 25
Displacement analsisanalytical met'od
A
6
C30o
A6,0 6C,20
@ector e)uation AB+BC=AC
{AB cos30AB sin30}+{BCcosBCsin}={AC0 }
sin=AB sin30
BC =38.68o
AC=74.53
=hen the an!le de!
sin=AB sin15
BC =18.87o
AC '=86.15
The displacement of C : 86.1574.53=11.62
E l % %
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Lecture Module 3 BDC4043 26
E$ample %&%
LL1
*
A
C
+ind the mathematical e)uations to calculate < and the distance *C#use vector analysis $. Plot the ma!nitude *C and the an!le for one cycle,L5L1 at *#b$ The intersection 'ith slider trac( is C1 #upper limit end$#c$ Dra' a circle >,L1 8L at *#d$ The intersection 'ith slider trac( is C #lo'er limit end$
R=ACOA
R=AC+OA
Trac( C
E$ample % ,
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Lecture Module 3 BDC4043 35
A
D
E$ample %&,
Air spray
*1 cm
2 cm
. cm
2 cm
2 cmC
The movement of a 'ater sprayer is automatically controlled by rotatin!the lever *A. Dra' the upper and lo'er positions of the sprayer boom DCand find the s'ayin! an!le of the boom.
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Lecture Module 3 BDC4043 36
*
D
C
A
6oom at upper position
R=ACOA
Trac( C
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Lecture Module 3 BDC4043 37
D
*
C1
A1
6oom at upper position
R=AC+OA
Trac( C
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Lecture Module 3 BDC4043 38
D
*
C1
C
47oMeasure this an!le
+imitin! position
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Lecture Module 3 BDC4043 39
! panalytical met'od
*
A
x
y
C
sin= y
L2L1
tan=y
x x=
y
tan
=asin y
L2L1
+imitin! position
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Lecture Module 3 BDC4043 40
! panalytical met'od
sin= y
L2+L1
tan=y
x x=
y
tan
=asin y
L2+L1
*
C1
A1
y
x
Complete ccle
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Lecture Module 3 BDC4043 41
p position and displacement diagram
The movement of a mechanism can be seen clearly if it simulated ina complete cycle. Any point can be eamined the cycle pattern.
/ !raphical method/ analytical approach
E$ample %&-
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Lecture Module 3 BDC4043 42
E$ample % -
A
6
C
D
9. cm
1. cm3. cm
2 cm9. cm
Dra' the initial settin!considerin! the correctdimensions
;imulate the movement
of the mechanism 'henA6 rotates CC=.The simulation must beat least cycle.#!raphical methodDra' every 30de!$
Plot the horiBontal andvertical positions ofpoint C #refer to D$
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Lecture Module 3 BDC4043 43
A
6
D
C
A6 CD CDy0 /0. 3.?
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Lecture Module 3 BDC4043 44
A
6
D
C
A6 CD CDy0 /0. 3.?
30 /1.1 3.2
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Lecture Module 3 BDC4043 45
A
6 D
C
A6 CD CDy0 /0. 3.?
30 /1.1 3.2
40 /3. 1.0
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Lecture Module 3 BDC4043 46
6
D
C
A
A6 CD CDy0 /0. 3.?
30 /1.1 3.2
40 /3. 1.0
?0 /3.? 0.2
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Lecture Module 3 BDC4043 47
A
6
DC
A6 CD CDy0 /0. 3.?
30 /1.1 3.2
40 /3. 1.0
?0 /3.? 0.2
10 /3.? /0.4
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Lecture Module 3 BDC4043 48
A
6
D
C
A6 CD CDy0 /0. 3.?
30 /1.1 3.2
40 /3. 1.0
?0 /3.? 0.2
10 /3.? /0.4
0 /2 /0.
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Lecture Module 3 BDC4043 49
A
6
D
C
A6 CD CDy0 /0. 3.?
30 /1.1 3.2
40 /3. 1.0
?0 /3.? 0.2
10 /3.? /0.4
0 /2 /0.
E0 /3.? 0.9
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Lecture Module 3 BDC4043 50
A
6
D
C
A6 CD CDy
0 /0. 3.?
30 /1.1 3.2
40 /3. 1.0
?0 /3.? 0.2
10 /3.? /0.4
0 /2 /0.
E0 /3.? 0.9
10 /3.4 .9
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Lecture Module 3 BDC4043 51
A
6
D
C
A6 CD CDy
0 /0. 3.?
30 /1.1 3.2
40 /3. 1.0
?0 /3.? 0.2
10 /3.? /0.4
0 /2 /0.
E0 /3.? 0.9
10 /3.4 .9
120 /1.9 3
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Lecture Module 3 BDC4043 52
A
6
D
C
A6 CD CDy
0 /0. 3.?
30 /1.1 3.2
40 /3. 1.0
?0 /3.? 0.2
10 /3.? /0.4
0 /2 /0.
E0 /3.? 0.9
10 /3.4 .9
120 /1.9 3
190 /0.1 3.?
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Lecture Module 3 BDC4043 53
A
6
D
C
A6 CD CDy
0 /0. 3.?
30 /1.1 3.2
40 /3. 1.0
?0 /3.? 0.2
10 /3.? /0.4
0 /2 /0.
E0 /3.? 0.9
10 /3.4 .9
120 /1.9 3
190 /0.1 3.?
300 .9 3.4
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Lecture Module 3 BDC4043 54
A
6D
C
A6 CD CDy
0 /0. 3.?
30 /1.1 3.2
40 /3. 1.0
?0 /3.? 0.2
10 /3.? /0.4
0 /2 /0.
E0 /3.? 0.9
10 /3.4 .9
120 /1.9 3
190 /0.1 3.?
300 .9 3.4
330 3.E
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Lecture Module 3 BDC4043 55
A
6
D
C
A6 CD CDy
0 /0. 3.?
30 /1.1 3.2
40 /3. 1.0
?0 /3.? 0.2
10 /3.? /0.4
0 /2 /0.
E0 /3.? 0.9
10 /3.4 .9
120 /1.9 3
190 /0.1 3.?
300 .9 3.4
330 3.E
340 /0. 3.?
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Lecture Module 3 BDC4043 56
A6 CD CDy
0 /0. 3.?
30 /1.1 3.2
40 /3. 1.0
?0 /3.? 0.2
10 /3.? /0.4
0 /2 /0.
E0 /3.? 0.9
10 /3.4 .9
120 /1.9 3
190 /0.1 3.?
300 .9 3.4
330 3.E
340 /0. 3.?
0 30 40 ?0 10 0 E0 10 120 190 300 330 340
/
/2
/3
/1
/
0
1
3PositionPoint C #/ais$ refer to D
rotation
PositionC#
/ais$
0 30 40 ?0 10 0 E0 10 120 190 300 330 340
/
0
1
3
2
PositionPoint C #y/ais$ refer to D
rotation
Position
C#
/ais$
E$ample %&.
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Lecture Module 3 BDC4043 57
Do the simulation in 7ample 3/4 by usin! &MPACT
Fints: dra' line in -iD. This 'ill be considered as rod element.The lin( should be defined only a sin!le element.
E$ample %&/
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Lecture Module 3 BDC4043 58
LL1
*
A
C
Plot the ma!nitude *C and the an!le for one cycle