problems the gear has the angular motion shown. determine the angular velocity and angular...
TRANSCRIPT
PROBLEM
SThe 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
=4 rad/s20.5 m
0.7 m
2 m
O
B
A C
PROBLEM
S
37o
37o
10 cm
20 cm
A
O
2
1
1=5 rad/s
C
16 cm
B
OABO
Link 1, of the plane mechanism shown, rotates about the fixed
point O with a constant angular speed of 5 rad/s in the cw
direction while slider A, at the end of link 2, moves in the circular
slot of link 1. Determine the angular velocity and the angular
acceleration of link 2 at the instant represented where BO is
perpendicular to OA. The radius of the slot is 10 cm.
Take sin 37=06, cos 37=0.8
PROBLEM
SFor the instant shown, particle A has a velocity of 12.5 m/s towards point C
relative to the disk and this velocity is decreasing at the rate of 7.5 m/s
each second. The disk rotates about B with angular velocity =9 rad/s and
angular acceleration =60 rad/s2 in the directions shown in the figure. The
angle remains constant during the motion. Telescopic link has a velocity of
5 m/s and an acceleration of 2.5 m/s. Determine the absolute velocity and
acceleration of point A for the position shown.
Problem 7
Velocity Analysis
j4.1i8.4v
j25
7i
25
245v
B
B
relBA vrvv
7
24
25
vB
Velocity Analysis
j6i6r
j3
2i
3
2k9r
m3
2x
9
2x
3
2
9
2xy 22
j10i5.7v
j5
4i
5
35.12v
rel
rel
3
4x2
dx
dytan
m3
2x
9
2x
3
2
9
2xy
3/2x
22
4
3
5
vrel
j4.17i3.6vA
Velocity Analysis
j7.0i4.2a
j25
7i
25
245.2a
B
B
relrelBA av2rraa
7
24
25
aB
Acceleration Analysis
j40i40j3
2i
3
2k60r
j54i54j6i6k9j3
2i
3
2k9k9r
m3
2x
9
2x
3
2
9
2xy 22
Acceleration Analysis
j135i180v2
j10i5.7k92v2
rel
rel
Acceleration Analysis
j6i5.4j5
4i
5
35.7a
j494.40i992.53j5
3i
5
449.67a
s/m49.67315.2
5.12va
trel
nrel
222
relnrel
m315.2
dxyd
dxdy
1
2dx
yd
3
4x2
dx
dy
2
2
2/32
2
2
3/2x
j794.74i892.254aA
4
3
5
(arel)t
vrel
+t+n
(arel)n
Acceleration Analysis
PROBLEM
SThe pin A in the bell crank AOD is guided by the flanges of the
collar B, which slides with a constant velocity vB of 0.9 m/s along
the fixed shaft for an interval of motion. For the position =30o
determine the acceleration of the plunger CE, whose upper end is
positioned by the radial slot in the bell crank. .
Problem 8
Velocity Analysis
)1(jvv CC
)2(jv5.0iv866.0j56.1i9.0v
j30sini30cosvj13.0i225.0k928.6vrvv
relrelC
relrelO/C
0
OC
vA
vA
vB=(vA)x
30o
s/rad928.615.0
039.1
s/m039.130cos
9.0
30cos
vv
AOD
BA
60o 30o
129.9 mm
vrel
(1)=(2) vrel=1.039 m/svc=2.079 m/s
vrel
2
AOD
AODtA2
AtA
2nAA
222nA
s/rad695.27
AOas/m154.430sinaa
s/m308.830cos
aa
s/m195.715.0928.6OAa
129.9 mm
aA
60o 30o
vrel(aA)n
30o
(aA)t
aA
VB=constant
So aA must be vertical.
)3(jaa CC
)4(ja5.0ia866.0j464.12i58.21a
j30sini30cosarelj30sin039.1i30cos039.1k928.62
j13.0i225.0k695.27j13.0i225.0k928.6k928.6a
av2rraa
relrelC
C
relrel
0
OC
Acceleration Analysis
(3)=(4)
arel=24.92 m/s2
aC=27.92 m/s2
PROBLEMS
1. The uniform 30-kg bar OB is secured to the accelerating frame in
the 30o position from the horizontal by the hinge at O and roller at A.
If the horizontal acceleration of the frame is a=20 m/s2, compute the
force FA on the roller and the x- and y-components of the force
supported by the pin at O.
PROBLEMS
2. The block A and attached rod have a combined mass of 60 kg and are
confined to move along the 60o guide under the action of the 800 N
applied force. The uniform horizontal rod has a mass of 20 kg and is
welded to the block at B. Friction in the guide is negligible. Compute the
bending moment M exerted by the weld on the rod at B.
SOLUTION
x
W=60(9.81) N
60o
N
FBDKinetic Diagram
x
2
.
/84.4
6060sin)81.9(60800
sma
amaF
x
xxforcesextx
FBD of rod
Bx
By
M
W1=20(9.81) N
KD of rod
mTax=60ax
m1ax=20ax
2/196
)60sin7.0)(94.4)(20(7.0)81.9(20
smM
MdmaM xB
PROBLEMS
3. The parallelogram linkage shown moves in the vertical plane with the
uniform 8 kg bar EF attached to the plate at E by a pin which is welded
both to the plate and to the bar. A torque (not shown) is applied to link
AB through its lower pin to drive the links in a clockwise direction. When
reaches 60o, the links have an angular acceleration an angular velocity
of 6 rad/s2 and 3 rad/s, respectively. For this instant calculate the
magnitudes of the force F and torque M supported by the pin at E.
PROBLEMS
4. The uniform 100 kg log is supported by the two cables and used as a
battering ram. If the log is released from rest in the position shown,
calculate the initial tension induced in each cable immediately after
release and the corresponding angular acceleration of the cables.
SOLUTION
W=100(9.81) N
FBD KD
TA TB
nam
tam
+n
+t
+n
+t
When it starts to move, v=0, =0 but ≠0 02 ran
2.
.
/905.430sin
57.849030cos0
smaammgamF
TTmgTTF
tttforcesextt
BABAforcesextn
2/45.22
905.4sradrat
Length of the cables
NTNT
TTTTM
BA
BABAkdG
17.63739.212
30)5.0(60sin)5.1(60sin0..
The motion of the log is curvilinear translation.
*
*
PROBLEMS
5. An 18 kg triangular plate is supported by cables AB and CD. When the
plate is in the position shown, the angular velocity of the cables is 4
rad/s ccw. At this instant, calculate the acceleration of the mass center
of the plate and the tension in each of the cables.
G10 cm
A
B
C
D60°60°
24
cm
20 cm 20 cm
Answer:
NTNT
sma
CDAB 93.7811.143
/23.6 2
PROBLEMS
6. The uniform 8 kg slender bar is hinged about a horizontal axis through
O and released from rest in the horizontal position. Determine the
distance b from the mass center to O which will result in an initial angular
acceleration of 16 rad/s2, and find the force R on the bar at O just after
release.
PROBLEMS
7. The spring is uncompressed when the uniform slender bar is in the
vertical position shown. Determine the initial angular acceleration a of
the bar when it is released from rest in a position where the bar has
been rotated 30o clockwise from the position shown. Neglect any sag of
the spring, whose mass is negligible.
SOLUTIONUnstrecthed length of the spring:
llllo 2
5)4/2( 22
When=30o , length of the spring:
llspring 2
3
When=30o , spring force:
2
3
2
5
2
3
2
5klllkFspring
(in compression)
l
g
m
k
lamml
lF
lmg
amIM
ltspring
tO
857.0864.0
412
1
2460cos
4
2
W
O
G+n
+t
On
Ot
30o
30o
l
Fspring
60o
.
lspringG
+n
+t
04
2 l
mam n
tamI
60o