7-dynamic force analysis
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Dynamic Analysis of Link Mechanism
Dr. TanveerDept. of MCT Engineering,
IIUM, Malaysia.
Figure 9.1 Dynamic analysis of a four-bar mechanism.
Dynamic analysis of afour-bar mechanism.
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,
The results for link 3 are,
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.
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,
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),
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.
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.
;
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.
Figure 9.7 Dynamic analysis of a slider crank mechanism.
Dynamic analysis of a slider crank mechanism.
;
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.
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