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