7-dynamic force analysis
DESCRIPTION
theory of machinesTRANSCRIPT
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Dynamic Analysis of Link Mechanism
Dr. TanveerDept. of MCT Engineering,
IIUM, Malaysia.
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Figure 9.1 Dynamic analysis of a four-bar mechanism.
Dynamic analysis of afour-bar mechanism.
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To complete a kinetic analysis. we must determine accelerations of the centers of mass of the moving links. Referring to Figure 9.1(a), and implementing Equation (9.1 - 1). The results for link 2 are,
The results for link 3 are,
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The results for link 3 are,
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xGx amF 22
yGy amF 22
xGxx amFF 221232
yGyy amFF 221232
0cossin 1222322232 MrFrF yx
02O
M+
+
+ (9.2-4)
(9.2-5)
(9.2-6)
Dynamic analysis of a four-bar mechanism.The governing equations of motion for link 2 are determined by considering the x and y components of forces and moment about fixed point (ground O2), where, M12 is input torque or driving torque.
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xGx amF 33
yGy amF 33
xGxx amFF 334323
yGyy amFF 334323
33333324
333334333323
33323
3coscos
sinsincos
sin
Gy
xy
x
IbrF
brFbF
bF
0
3GM+
+
+ (9.2-7)
(9.2-8)
(9.2-9)
Dynamic analysis of a four-bar mechanism.
The governing equations of motion for link 3 are determined by considering the x and y components of forces and moment about centroid G3,
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xGx amF 44
yGy amF 44
xGxx amFF 441434
yGyy amFF 441434
04O
M+
+
+ (9.2-10)
(9.2-11)
424424344434 4
cossin bmIrFrF Gyx (9.2-12)
Dynamic analysis of a four-bar mechanism.
Transformation of moment of inertia from center of gravity G4 to the fixed point O4.
The governing equations of motion for link 4 are determined by considering the x and y components of forces and moment about fixed point (ground O4),
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xGxx amFF 221232
yGyy amFF 221232
0cossin 1222322232 MrFrF yx
xGxx amFF 334323
yGyy amFF 334323
33333324
3333343
3332333323
3coscos
sinsin
cossin
Gy
x
yx
IbrF
brF
bFbF
xGxx amFF 441434
yGyy amFF 441434
4
244
24344434
4
cossin
bmI
rFrF
G
yx
;
0000000
010100000
001010000
00000
00011000
000010100
1000000
000001010
000000101
6,95,9
6,65,64,63,6
4,33,3
AA
AAAA
o
AA
A
121414343423231212 MFFFFFFFF yxyxyxyx
;sin 223,3 rA 224,3 cosrA
;sin 3333,6 bA ;cos 3334,6 bA
;sinsin 333335,6 brA
;coscos 333336,6 brA
;sin 445,9 rA 446.9 cosrA
Dynamic analysis of a four-bar mechanism.
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xGxx amFF 221232
yGyy amFF 221232
0cossin 1222322232 MrFrF yx
xGxx amFF 334323
yGyy amFF 334323
33333324
3333343
3332333323
3coscos
sinsin
cossin
Gy
x
yx
IbrF
brF
bFbF
xGxx amFF 441434
yGyy amFF 441434
4
244
24344434
4
cossin
bmI
rFrF
G
yx
;
12
14
14
34
34
23
23
12
12
M
F
F
F
F
F
F
F
F
X
y
x
y
x
y
x
y
x
4244
4
4
3
3
3
2
2
4
4
4
3
3
3
2
2
0
bmI
am
am
I
am
am
am
am
B
G
yG
xG
G
yG
xG
yG
xG
Dynamic analysis of a four-bar mechanism.
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;
0000000
010100000
001010000
00000
00011000
000010100
1000000
000001010
000000101
6,95,9
6,65,64,63,6
4,33,3
AA
AAAA
o
AA
A
;
12
14
14
34
34
23
23
12
12
M
F
F
F
F
F
F
F
F
X
y
x
y
x
y
x
y
x
4244
4
4
3
3
3
2
2
4
4
4
3
3
3
2
2
0
bmI
am
am
I
am
am
am
am
B
G
yG
xG
G
yG
xG
yG
xG
;sin 223,3 rA 224,3 cosrA
;sin 3333,6 bA ;cos 3334,6 bA
;sinsin 333335,6 brA
;coscos 333336,6 brA
;sin 445,9 rA 446.9 cosrA
Dynamic analysis of a four-bar mechanism.
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Figure 9.7 Dynamic analysis of a slider crank mechanism.
Dynamic analysis of a slider crank mechanism.
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;
01100000
00010000
0000
0011000
00010100
100000
00001010
00000101
6,65,64,63,6
4,33,3
AAAA
o
AA
A
;
12
14
34
34
23
23
12
12
M
F
F
F
F
F
F
F
X
y
y
x
y
x
y
x
0
0
4
3
3
3
2
2
4
3
3
3
2
2
xG
G
yG
xG
yG
xG
am
I
am
am
am
am
B
;sin 223,3 rA 224,3 cosrA
;sin 3335,6 bA ;cos 3336,6 bA
;sinsin 333333,6 brA ;coscos 333334,6 brA
Dynamic analysis of a slider crank mechanism.