PROBLEMS1. Determine the angular velocity of link OB if the piston has a velocity of 2 m/s to the

right at the instant shown.

Instantaneous Center of Zero Velocity

PROBLEMS2. If the velocity of point A is 3 m/s to the right, determine the velocity of point B andangular velocity of the bar.

Instantaneous Center of Zero Velocity

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.

Instantaneous Center of Zero Velocity

vB

P (IC for AB)

vA

vO

30o

30o

PAB

m.ABAPsin

AB

sin

PB

sin

AP60

3012030

m.cos.PB 039130602

C (IC for Gear)

s/rad..OC

vOgear 14357

1750

10

s/rad..

.

AP

vAAB 5728

60

14317

s/m....ACv gearA 143171750125014357

s/m.PBv ABB 6929

AB

4. The flexible band F is attached at E to the rotating

sector and leads over the guide pulley. Determine

the angular velocities of AD and BD for the position

shown if the band has a velocity of of 4 m/s.

Point O: IC for member OAE (Absolute IC)Point B: IC for link BD (Absolute IC)Point C : IC for link AD (Relative IC)

FvAv

s/m..OAv

s/rad.

OA

OA

A 52125020

2020

4

Dv

C

OA

AD

BD

s/rad..

.

AC

vA

AD512

20

52

s/m...CDvADD 8751150512

s/rad..

.

BD

vD

BD57

250

8751

5. The oil pumping unit consists of a walking beam AB, connecting rod BC, and crank CD. If the crank rotates at a

constant rate of 6 rad/s (counterclockwise), determine the speed of the rod hanger H at the instant shown. Also find

the angular velocities of members BC and AB.

vC

vB

vH

a

BC

P(IC for BC – connecting rod)

ICs : D (for CD), E (for AB) P (for BC)

aa

o..

.tan 469

72

450 aa

18 m

s/m..CDv CDC 45906

mtan

CP 183

a

s/rad..

BP

v

CP

vBC

BCBC 30

18

45

s/m..BPv

.

BCB 474518330

24818

22

E (IC for AB -walking beam)

s/rad

..

.

EB

v

.

BAB 2

45072

4745

7372

22

s/m..AEv ABH 45722

6. In relation to the elongation of the hydraulic piston AC, the velocity of point A on the

slider is v = 1.25 m/s for the instant when q=36.87o. At this moment BD is horizontal and DE

is vertical. Determine the angular velocities of arms BD and DE and the hydraulic piston AC

for this instant.

200 mm

q

200 mm vD

vB

P (IC for BD)

q

7. Motion of the roller A against its restraining spring is controlled by the downward

motion of the plunger E. For an interval of motion the velocity of E is v = 0.2 m/s.

Determine the velocity of A when q becomes 90°.

Instantaneous Center of Zero Velocity

8. 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.

Instantaneous Center of Zero Velocity

vD

(IC for DOA)P

vo=1.2 m/s

vA

a

D

O C375 mm

q = 45° a

o.sinsin

141745

300125 a

a

mmCO

.coscosCO

375

141730045125

mm.tanPO 6115375 a

s/rad..

.

PO

vODOA 3810

11560

21 s/m....PAv DOAA 762150115603810

(IC for DC)

P

OCa

375 mm