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PROBLEM 15.148*
A wheel of radius r rolls without slipping along the inside of a fixed cylinder
of radius R with a constant angular velocity
.ω
Denoting by P the point of the
wheel in contact with the cylinder at
0,t=
derive expressions for the
horizontal and vertical components of the velocity of P at any time t. (The
curve described by Point P is a hypocycloid.)
PROBLEM 15.149*
In Problem 15.148, show that the path of P is a vertical straight line when
/2.
rR=
Derive expressions for the corresponding velocity and acceleration of
P at any time t.
PROBLEM 15.150
Pin P is attached to the collar shown; the motion of the pin is guided by a
slot cut in rod BD and by the collar that slides on rod AE. Knowing that
at the instant considered the rods rotate clockwise with constant angular
velocities, determine for the given data the velocity of pin P.
8
AE
ω
=
rad/s,
3
BD
ω
=
rad/s
PROBLEM 15.151
Pin P is attached to the collar shown; the motion of the pin is guided by
a slot cut in rod BD and by the collar that slides on rod AE. Knowing that
at the instant considered the rods rotate clockwise with constant angular
velocities, determine for the given data the velocity of pin P.
7
AE
ω
=
rad/s,
4.8
BD
ω
=
rad/s
PROBLEM 15.152
Two rotating rods are connected by slider block P. The rod
attached at A rotates with a constant angular velocity
.
A
ω
For the
given data, determine for the position shown (a) the angular
velocity of the rod attached at B, (b) the relative velocity of slider
block P with respect to the rod on which it slides.
b = 8 in.,
6 rad/s.
A
ω
=
PROBLEM 15.153
Two rotating rods are connected by slider block P. The rod
attached at A rotates with a constant angular velocity
.
A
ω
For
the given data, determine for the position shown (a) the
angular velocity of the rod attached at B, (b) the relative
velocity of slider block P with respect to the rod on which it
slides.
b = 300 mm,
10 rad/s.
A
ω
=
PROBLEM 15.154
Pin P is attached to the wheel shown and slides in a slot cut in bar
BD. The wheel rolls to the right without slipping with a constant
angular velocity of 20 rad/s. Knowing that x = 480 mm when
0,
θ
=
determine the angular velocity of the bar and the relative
velocity of pin P with respect to the rod for the given data.
(a)
0,
θ
=
(b)
90 .
θ
= °
PROBLEM 15.154 (Continued)
PROBLEM 15.155
Knowing that at the instant shown the angular velocity of bar
AB is 15 rad/s clockwise and the angular velocity of bar EF is
10 rad/s clockwise, determine (a) the angular velocity of rod
DE, (b) the relative velocity of collar B with respect to rod DE.
PROBLEM 15.156
Knowing that at the instant shown the angular velocity of rod
DE is 10 rad/s clockwise and the angular velocity of bar EF is
15 rad/s counterclockwise, determine(a) the angular velocity of
bar AB, (b) the relative velocity of collar B with respect to rod
DE.
