1. if the velocity of point a is 3 m/s to the right...
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1. 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
2. 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.
Instantaneous Center of Zero Velocity
FvAv
s/m..OAv
s/rad.
OA
OA
A 52125020
2020
4
Dv
C
OA
AD
BD
s/rad..
.
AC
vA
AD512
20
52
the band has a velocity of of 4 m/s
s/m...CDvADD 8751150512
s/rad..
.
BD
vD
BD57
250
8751
Point O: IC for member OAE (Absolute IC)Point B: IC for link BD (Absolute IC)Point C : IC for link AD (Relative IC)
3. 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
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
vC
vB
vH
a
BC
ICs : D (for CD), E (for AB) , P (for BC)
aa
o46.9a
18 m
E (IC for AB -walking beam)
srad
EB
v
AB
BAB
/2
45.07.2
474.5
737.2
22
s/m..AEv ABH 45722
smvB /474.5
4. 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
vA
vB
A
B
O
D
ICs : O (for OB)
P (for DBA)
P
DBA
vA
vB
A
B
O
D
P
DBA
150 mm
vD
20
0 m
m
a
b
s/m...v
APv
A
DBAA
2770203861
o.tan 5620160
60aa
o.8736o.1353
o.. 5732873690 ab
s/m..cos
.
cos
vvD 2370
5732
20
b
mm.DP 8817060160 22
s/rad..
.
DP
vDDBA 3861
170880
2370
vDv b
b
5. Determine the angular acceleration of link EC in the position shown, where
and when qb=60o. Pin A is fixed to link EC.
The circular slot in link DO has a radius of curvature of 150 mm. In the position
shown, the tangent to the slot at the point of contact is parallel to AO.
srad /2 b 2/6 sradb
150 mm
mm150AC
Motion Relative to Translating&Rotating Axes
6. In the mechanism shown, crank AO rotates at an angular velocity of 4 rad/s (clockwise) andangular acceleration 5 rad/s2 (clockwise) by a torque T. The masses of uniform bar AB, piston B andcrank AO are mAB=6 kg, mpiston=2 kg, and mAO=10 kg, respectively. Radius of gyration of crank AOabout the center of gravity is 0.1 m. Determine, angular velocity and angular acceleration of bar AB,reactions supported by the pins A and B. Also determine the torque T.Mechanism lies on the horizontal plane!
AB=1.333 rad/s (ccw)aAB=3 rad/s2 (ccw)aB=11.233 m/s2 (↓)
Kinetics of Rigid Bodies