1. the mechanism shown is used in a - dokuz eylül...
TRANSCRIPT
1. The mechanism shown is used in ariveting machine. It consists of a drivingpiston A, three links, and a riveter whichis attached to the slider block D.Determine the velocity of D at the instantshown, when the piston at A is travelingvA=20 m/s.
Instantaneous Center of Zero Velocity
11 CP
v
AP
v CAAC
Cv
DvP2 (IC of link CD)
P1 (IC of link AC)
AC
15o
mmCP
mmAP
615.111975sin11.1159
11.115975cos
300
1
1
P1 (IC of link AC)
sradAC /86.171159.1
20
smCPv ACC /318.191
AC
Cv
DvP2 (IC of link CD)
P1 (IC of link AC)
15o
smvC /318.19
AC
P2 (IC of link CD)
22 DP
v
CP
v DCCD
P2D
C
45o
CD
mmCP
mmDP
CPDP
474.122
828.44
45sin15sin120sin
150
2
2
22
smvD /07.7474.122
828.44318.19
2. The disk D rolls to the left without slipping
and has an angular velocity of 3 rad/s.
Determine the angular velocity of link AB and
the velocity of center of disk E. Use the
Method of Instantaneous Center of Zero
Velocity.
60o
=3 rad/s
45o
R
R
0.4 m
0.3 m
3R
A
B
D E
R=0.5 m
O1 O2
Instantaneous Center of Zero Velocity
60o
=3 rad/s
45o
R
R
0.4 m
0.3 m
3R
A
B
D E
R=0.5 m
O1 O2
Bv
C2 (IC of disk E)
15o
AC
P (IC of link AB)
C1 (IC of disk D)
Av
AB
3. The gear has the angular motion shown. Determine the angular velocity and angular acceleration
of the slotted link BC at this instant. The pin at A is fixed to the gear.
=2 rad/s
a=4 rad/s20.5 m
0.7 m
2 m
O
B
A C
Motion Relative to Rotating Axes
Kinetics of Rigid Bodies
AB=1=10 rad/s (cw)BC=2.5 rad/s (ccw)aBC=21.09 rad/s2 (ccw)ac=21.204 m/s2 (↑)
4. A compressor is shown in the figure. Member AB is rotating at a constant angular velocity of 10
rad/s. Member BC has a mass of 2 kg and piston C has a mass of 1 kg. The pressure p on the circular
surface of the piston is 10 kPa. At the instant shown, what are the forces transmitted by pins B and C?
5. The mechanism used in a marine engine consists of a single crank AB and two connecting rodsBC and BD. Determine the velocity of the pistons at C and D and angular velocities of rods BC andBD when the crank is in the position shown and has an angular velocity of 5 rad/s.
s/m.ABv ABB 1205
Cv
Dv
P2 (IC of link BD)
P1 (IC of link BC)
Instantaneous Center of Zero Velocity
0.5 m
s/m.v
ABv
B
ABB
1205
Dv
P2 (IC for link BD)
P2
D
B
30o
105o
45o
0.6
83
m
s/m.v
s/rad.
.
v
.
v
D
BD
DBBD
5180
4641
35406830
1
0.5 m
m.DPm.BP
sin
DP
sin
BP
sin
.
35406830
3010545
50
22
22
s/m.v
ABv
B
ABB
1205
Cv
Dv
P1 (IC for link BC)
P1
C
B60o
75o
45o
0.5
46
m
smv
srad
vv
C
BC
CBBC
/896.0
/8315.1
489.0546.0
1
0.5 m
m.BPm.CP
sin
BP
sin
CP
sin
.
54604890
756045
40
11
11
6. The unbalanced 20 kg wheel with the mass center at G has a radius of gyration
about G of 202 mm. The wheel rolls down the 20o incline without slipping. In the
position shown. The wheel has an angular velocity of 3 rad/s. Calculate the friction
force F acting on the wheel at this position.
Kinetics of Rigid Bodies
“General Motion”FBD
N
mg
Ff
KD
=
am
aI
222
8160202020 mkg.).(kmI
aa 25.0 raox x
y
j.i..i.kki.ki.aaa
yx
aa
O/GOG
075067502500750330750250 aaa
604805
67502502020
.F
..FsinmgamF
f
fxefx
a
a
a
a51367184
07502020
..N
.cosmgNamF yefy
aa 81602500750 .).(F).(NIM fefGN.N
N.F
s/rad.
f
971160
6172
59715 2
a❷
❸
❶