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PROBLEM 15.133
Knowing that at the instant shown bar AB has an angular
velocity of 4 rad/s and an angular acceleration of 2 rad/s2, both
clockwise, determine the angular acceleration (a) of bar BD,
(b) of bar DE by using the vector approach as is done in Sample
Problem 15.16.
BE DE BD BD
PROBLEM 15.133 (Continued)
DE
PROBLEM 15.134
Knowing that at the instant shown bar AB has an angular velocity of 4 rad/s
and an angular acceleration of 2 rad/s2, both clockwise, determine the angular
acceleration (a) of bar BD, (b) of bar DE by using the vector approach as is
done in Sample Problem 15.16.
SOLUTION
BD
PROBLEM 15.134 (Continued)
DE
PROBLEM 15.135
Robert’s linkage is named after Richard Robert (1789–1864) and can be used
to draw a close approximation to a straight line by locating a pen at Point F.
The distance AB is the same as BF, DF and DE. Knowing that at the instant
shown bar AB has a constant angular velocity of 4 rad/s clockwise, determine
(a) the angular acceleration of bar DE, (b) the acceleration of Point F.
6
BD DE
BD
PROBLEM 15.135 (Continued)
Acceleration Analysis:
0
AB
=α
2
F
PROBLEM 15.136
For the oil pump rig shown, link AB causes the beam
BCE to oscillate as the crank OA revolves. Knowing
that OA has a radius of 0.6 m and a constant
clockwise angular velocity of 20 rpm, determine the
velocity and acceleration of Point D at the instant
shown.
SOLUTION
Units: meters, m/s, m/s2
PROBLEM 15.136 (Continued)
Equating like components of
B
α
expressed by Eqs. (1) and (2),
/
D EC t
D
PROBLEM 15.137
Denoting by
A
r
the position vector of Point A of a rigid slab that is in plane
motion, show that (a) the position vector
C
r
of the instantaneous center of rotation is
2
A
CA
ω
×
= + ωv
rr
where
ω
is the angular velocity of the slab and
A
v
is the velocity of Point A,
(b) the acceleration of the instantaneous center of rotation is zero if, and only if,
AA A
α
ω
= +×avωv
where
α
=kα
is the angular acceleration of the slab.
PROBLEM 15.138*
The drive disk of the scotch crosshead mechanism shown has an angular
velocity
ω
and an angular acceleration
α
, both directed counterclockwise.
Using the method of Section 15.4 B, derive expressions for the velocity and
acceleration of Point B.
B
B
PROBLEM 15.139*
The wheels attached to the ends of rod AB roll along the
surfaces shown. Using the method of Section 15.4 B, derive an
expression for the angular velocity of the rod in terms of
, ,,
B
vl
θ
and
β
.
PROBLEM 15.140*
The wheels attached to the ends of rod AB roll along the
surfaces shown. Using the method of Section 15.4 B and
knowing that the acceleration of wheel B is zero, derive an
expression for the angular acceleration of the rod in terms of
, ,,
B
vl
θ
and
β
.
SOLUTION
B
dl
PROBLEM 15.141*
A disk of radius r rolls to the right with a constant velocity v. Denoting by P the point of the rim in contact
with the ground at
0,t=
derive expressions for the horizontal and vertical components of the velocity of P at
any time t.
Py
y
PROBLEM 15.142*
Rod AB moves over a small wheel at C while end A moves to the
right with a constant velocity vA. Using the method of Section
15.4 B, derive expressions for the angular velocity and angular
acceleration of the rod.
PROBLEM 15.143*
Rod AB moves over a small wheel at C while end A moves to
the right with a constant velocity vA. Using the method of
Section 15.4 B, derive expressions for the horizontal and
vertical components of the velocity of Point B.
( )
3/2
22
By
A
bx
+
PROBLEM 15.144
Crank AB rotates with a constant clockwise angular velocity
.ω
Using the method of Section 15.4 B, derive expressions for the
angular velocity of rod BD and the velocity of the point on the rod
coinciding with Point E in terms of
,
θ
,
ω
b, and l.
22
2 cos
BD
l b bl
θ
Differentiate the expression for
2.u
2 2 sin
uu bl
θθ
= −
22
2 cos
E
l b bl
θ
lb
θ
+
PROBLEM 15.145
Crank AB rotates with a constant clockwise angular velocity
.ω
Using the method of Section 15.4 B, derive an expression for the
angular acceleration of rod BD in terms of
,
θ
,
ω
b, and l.
2 cos
l b bl
θ
PROBLEM 15.146
Solve the engine system from Sample Prob. 15.15 using the methods of
Section 15.4B. Hint: Define the angle between the horizontal and the
crank AB as
θ
and derive the motion in terms of this parameter.
SOLUTION
D=a
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
PROBLEM 15.147*
The position of rod AB is controlled by a disk of radius r that is attached to yoke CD.
Knowing that the yoke moves vertically upward with a constant velocity v0, derive
expression for the angular velocity and angular acceleration of rod AB.
PROBLEM 15.147* (Continued)
r
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