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Instantaneous Center of Zero Velocity
Problems
PROBLEMS
1. A device which tests the resistance to wear of two materials A and B is shown. If the link EO has a velocity of 1.2 m/s to the right when q = 45°, determine the rubbing velocity vA.
PROBLEMS vEO =1.2 m/s to the right when q = 45°, determine the rubbing velocity vA.
P wOAD C
300D
P
O
45 125
PROBLEMS 2. Horizontal oscillation of the spring loaded plunger E is controlled by varying the air pressure in the horizontal pneumatic cylinder F. If the plunger has a velocity of 2 m/s to the right when q = 30°, determine the downward velocity of vD of roller D in the vertical guide and find the angular velocity w of ABD for this position.
PROBLEMS vE = 2 m/s to the right when q = 30°, determine the downward velocity of vD of roller D and w of ABD .
P
30°
30°
200
2.173
2.173100
30°
PROBLEMS
3. If the center O of the gear is given a velocity of vO = 10 m/s, determine the velocity of the slider block B at the instant shown.
PROBLEMS
mBP
mABAP
ABBPAP
039.130cos)6.0(2
6.0
30sin120sin30sin
sm
v
srad
gearA
gear
/143.17
175.0125.0
/143.57175.0
10
300.0
w
w
smBPv
sradAP
v
ABB
AAB
/69.29
/57.28
w
w
vO = 10 m/s, determine vB .
vO
A vA
C
vB
P
30°
wAB
120°
30° B
PROBLEMS 4. The mechanism used in a marine engine consists of a single crank AB and two connecting rods BC and BD. Determine the velocity of the pistons at C and D and angular velocities of rods BC and BD when the crank is in the position shown and has an angular velocity of 5 rad/s.
s/m.ABv ABB 1205 w
Cv
Dv
P2 (IC of link BD)
P1 (IC of link BC)
0.5 m
s/m.ABv ABB 1205 w
Cv
Dv
P2 (IC for link BD)
P1 (IC for link BC) P2
D
B
30o
105o
45o
0.6
83 m
s/m.v
s/rad.
.
v
.
v
m.DP
m.BP
sin
DP
sin
BP
sin
.
D
BD
DBBD
5180
4641
35406830
1
3540
6830
3010545
50
2
2
22
w
w
P1
C
B 60o
75o
45o
0.5
46 m
smv
srad
vv
mBP
mCP
BPCP
C
BC
CBBC
/896.0
/8315.1
489.0546.0
1
546.0
489.0
75sin60sin45sin4.0
1
1
11
w
w
0.5 m
PROBLEMS 5. The mechanism shown is used at a riveting machine. The mechanism consists of a drive piston A, three links and sliding block D. If the velocity of piston at the instant shown is vA = 20 m/s, determine the angular velocity of link CD and the velocity of block D, vD. Use the Method of Instantaneous Center of Zero Velocity.
20 m/s
15
PROBLEMS
vA = 20 m/s, wCD = ?, vD = ?
20 m/s
20 m/s
45
PAC
PDC
PROBLEMS 6. The center O of the stepped disk which rolls on the horizontal surface without slipping has a velocity of 6 m/s to the right at the instant considered. The disk contacts the surface at point C. Rod AB, attached to the disk with a pin connection at point A is also pin connected to a small roller at B. The roller B can move freely on the circular road which has a radius of 120 cm. Determine the angular velocity of rod AB (wAB) and the velocity of roller B (vB) for this instant.
O vO=6 m/s
r
R
60o
240 cm
100 cm
A
C
120 cm
B
37o
r=30 cm R= 50 cm
PROBLEMS v0 = 6 m/s (→), wAB = ? vB = ?
O vO=6 m/s
r
R
60o
240 cm
100 cm
A
C
120 cm
B
37o
r=30 cm R= 50 cm
A
O
C
60
30
50
120
79.5190
21.38,6186.0sin,120sin
70sin50
70
120cos305023050 222
cmAC
AC
A
B
100
240
62.22
417.0240100
tan
cmAB 260100240 22
P
A
B
P
C79.51
3721.38
62.75
260
Bv
Av