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Static Force Analysis for Skid Loader - Scalar
A trunnion mount hydraulic cylinder actuates the arm of a skid steer loader as shown below. At this position, e = 40 inches, = 61.131°, e = -12 ips, ^ = -0.3625 rad/s.
Determine the force on the hydraulic cylinder required to lower an 800 lbf payload attached to point D by a cable. The payload moves with constant velocity at the position shown. You may neglect the effects of friction. The weight of the arm and cylinder are small compared to the payload. Show your work.
FCYLINDER __________________________
What corresponding hydraulic pressure would be required for a cylinder with a 3 inch DIA bore?
PCYLINDER __________________________
Is this value reasonable? Why?
If you include friction between the piston and cylinder wall, will it increase or decrease your computation for pressure.
increase decrease Why?
What value would you use for the coefficient of friction between the piston and cylinder wall?
_________________________________ Why?
Should your analysis be different if the cylinder were retracting at constant velocity instead of the payload moving at constant velocity?
yes no Why?
A
B
C
e
Not to scale AB = 36 inches AC = 42 inches AD = 96 inches = 16°
D
Payload
sin / AB = sin / e = 52.01° = 77.131°
∑M on 4 about A CCW+ -(FC sin ) AC +(P sin() AD = 0 FC = 2261.9 lbf
2261.9 lbf up/left
320 psi A = D^2 / 4 = 7.069 in^2
OK, industrial hydraulics often go to 3000 psi
pressure pushes up friction force will be up opposing piston motion
0.1 lubricated
constant e^ means ^ will not be constant means velocity of the payload will not be constant, therefore must account for acceleration of payload mass
P
D
C
F 14 y F 14 x
A
FC
Static Force Analysis for Four Bar - Scalar
M on 4 about D CCW+
- F 34 x^ (CD) sin 65.173- F 34 y^ (CD) sin 24.827 + FQ (DQ) sin 77 = 0 40.842 F 34 x^ + 18.895 F 34 y^ = 4676.98 N
M on 3 about B CCW+
- F 43 x^ (BC) sin 13.151 + F 43 y^ (BC) sin 76.849 + FP (BP) sin 60 = 0
- 13.651 F 43 x^ + 58.426 F 43 y^ = -2987.78 N
F on 4 right + F 34 x^ - FQ cos 37.827 + F 14 x^ = 0 F 14 x^ = 75.980 N F on 4 up + F 34 y^ - FQ sin 37.827 + F 14 y^ = 0 F 14 y^ = 52.360 N F on 3 right + F 43 x^ - FP cos 46.849 + F 23 x^ = 0 F 23 x^ = 184.580 N F on 3 up + F 43 y^ + FP sin 46.849 + F 23 y^ = 0 F 23 y^ = -39.138 N
M on 2 about A CCW+ - F 32 x^ (AB) sin 65 + F 32 y^ (AB) sin 25 + T 12 = 0 T 12 = - 5514.8 N.cm F on 2 right + F 12 x^ + F 32 x^ = 0 F 12 x^ = 184.580 N F on 2 up F 12 y^ + F 32 y^ = 0 F 12 y^ = -39.138 N
F (^) Q = 200 N F 34 x
F 34 y
24.827
65.173
F 14 y
F 14 x
65.173
24.827
77
D
C
CD = 45 cm DQ = 24 cm CQ = 21 cm
Q
37.827
F 43 y
F 43 x F 23 x
76.849 F 23 y
13.151
46.849
B
C
F (^) P = 150 N
BC = 60 cm BP = 23 cm CP = 37 cm
P
13.151 60
76.849
70.295N
81.993N
F
F
2987.78N
4676.98N
F
F
y 34
x 34 y 34
x 34
F 12 x
AB = 30 cm
F 32 y
F 32 x
F 12 y 65
25
A
B
T 12 25
65
A 65
T 12
D
77
60
C B P
Q
F (^) Q = 200 N
F (^) P = 150 N AB = 30 cm BC = 60 cm CD = 45 cm AD = 90 cm BP = 23 cm DQ = 24 cm
3 4
2
1 D 1
13.151
65.173
Static Force Analysis for Four Bar - Matrix
F on 2 right + F 12 x^ + F 32 x^ = 0 F on 2 up + F 12 y^ + F 32 y^ = 0 M on 2 about A CCW + - F 32 x^ r (^) B/Ay^ + F 32 y^ r (^) B/Ax^ + T 12 = 0 F on 3 right + F 23 x^ + F 43 x^ + FPx^ = 0 F on 3 up + F 23 y^ + F 43 y^ + FPy= 0 M on 3 about P CCW + - F 23 x^ r (^) B/Py^ + F 23 y^ r (^) B/Px^ - F 43 x^ r (^) C/Py^ + F 43 y^ r (^) C/Px^ = 0
F on 4 right + F 34 x^ + F 14 x^ + FQx^ = 0 F on 4 up + F 34 y^ + F 14 y^ + FQx^ = 0 M on 4 about Q CCW + - F 34 x^ r (^) C/Qy^ + F 34 y^ r (^) C/Qx^ - F 14 x^ r (^) D/Qy^ + F 14 y^ r (^) D/Qx^ = 0
F
F
F
F
T
F
F
F
F
F
F
F
F
0 0 0 0 r r r r 0
0 0 r r r r 0 0 0
0 0 r r 0 0 0 0 1
y Q
x Q
y P
x P
12
14 y
14 x
34 y
34 x
23 y
23 x
12 y
12 x
x D/Q
y D/Q
x C/Q
y C/Q
x C/P
y C/P
x B/P
y B/P
x B/A
y B/A
FP
= 150 N @ 133.151 = - 102.589 + j 109.433 N FQ
= 200 N @ 217.827 = - 157.973 - j 122.656 N B/A = 30 cm @ 65 = 12.678 + j 27.189 cm B/P = 23 cm @ 193.151 = -22.396 - j 5.233 cm C/P = 37 cm @ 13.151 = 36.030 + j 8.418 cm C/Q = 21 cm @ 114.827 = -8.817 + j 19.059 cm D/Q = 24 cm @ -65.173 = 10.077 - j 21.782 cm
F 12 x
F 32 y
F 32 x
F 12 y 65 A
B T 12
F 43 y
F 43 x F 23 x
F 23 y
B
C
F (^) P = 150 N
P 13.151
60 46.849
F 14 y
F (^) Q = 200 N F 34 x
F 34 y
F 14 x
65.173
77
D
C
Q
37.827
T
F
F
F
F
F
F
F
F
12
y 14
x 14
x 34
34 x
23 y
23 x
12 y
12 x
52.36N
75. 98 N
70.29N
82.00N
- 39.14N
184.59N
- 39.14N
184.59N
T
F
F
F
F
F
F
F
F
12
y 14
x 14
x 34
x 34
y 23
x 23
y 12
x 12
F on 2 right + F 12 x^ + F 32 x^ = 0 F on 2 up + F 12 y^ + F 32 y^ = 0 M on 2 about A CCW + - (F 32 x^ sin 45°) AB + (F 32 y^ sin 45°) AB + T 32 = 0 F on 3 right + F 23 x^ + F 43 x^ = 0 F on 3 up + F 23 y^ + F 43 y^ = 0 M on 3 about B CCW + - (F 43 x^ sin 30.86°) BC - (F 43 y^ sin 59.14°) BC + T 23 = 0
F on 4 right + F 34 x^ + F 14 x^ = 0 F on 4 up + F 34 y^ + F 14 y^ - W 4 = 0 M on 4 about D CCW + - (F 34 x^ sin 15.76°) CD - (F 34 y^ sin 74.24°) CD + (W 4 sin 74.24°) DG 4 = 0
F 12 x
F 12 y
45
A
F 32 y
B F^32 x
T 32
45
45
45
F 43 y F 43 x
F 23 x
F 23 y
B
C (^) 30.86
30.86
59.14
59.14 T 23
F 14 y
F 34 x
F 34 y
74.24 F^14 x
D
C (^) G (^4)
15.76
15.76
74.24
W (^4)
74.24
4
4
4
x 12 y 12 x 23 y 23 x 34 y 34 x 14 y 14 32
DG)
sin W(
0000000 W
F F F F F F F F T
sin CD
sin CD
sin BC
sin BC
sin AB
sin AB 0 0
F F F F F F F F T
x 12 y 12 x 23 y 23 x 34 y 34 x 14 y 14 32
lbf. in 1 . 1351
lbf 1 . 50
lbf 3 . 29
lbf (^9). 129
lbf (^3). 29
lbf (^9). 129
lbf (^3). 29
lbf (^9). 129
lbf (^3). 29
xF 12 yF 12 xF 23 yF 23 xF 34 yF 34 xF 14 yF (^14) T 32
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Static Force Analysis for Slider Crank - Matrix
F on 2 right + F 12 x^ + F 32 x^ = 0 F on 2 up + F 12 y^ + F 32 y^ = 0 M on 2 about A CCW + - (F 32 x^ sin) AB + (F 32 y^ cos) AB + T 12 = 0 F on 3 right + F 23 x^ + F 43 x^ + FQx^ = 0 F on 3 up + F 23 y^ + F 43 y^ + FQy^ = 0 M on 3 about Q CCW + -(F 23 x^ sin) BQ -(F 23 y^ cos) BQ +(F 43 x^ sin) CQ +(F 43 y^ cos) CQ = 0
F on 4 right + F 14 x^ + F 34 x^ + P = 0 F on 4 up + F 14 y^ + F 34 y^ = 0 friction F 14 x^ = - F 14 y^ sign(VC )
P
F
F
T
F
F
F
F
F
F
F
F
0 0 0 0 0 0 1 sign(V ) 0
0 0 BQsin BQcos CQsin CQcos 0 0 0
0 0 ABsin ABcos 0 0 0 0 1
Qy
Qx
12
14 y
14 x
34 y
34 x
23 y
23 x
12 y
12 x
C
2 A
B
T 12^
F 32 y
F 12 y
F 12 x
F 32 x
F 23 y
1 1
2
3
A^4
B
P
T 12 Q Q
C
B^
3
F 23 x
C
FQy FQx F 43 y Q F 43 x
(^4) P
F 14 x F 14 y
- direction for impending V (^) C to right F 34 y C F^34 x
(^121223233434141412)
F F F F F F F F T
x y x y x y x y
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