EGR 232 Lecture 23 Homework Fall 2013Chap. 15, Problem 40Small wheels have been attached to the ends of rod AB and roll freely along the surfaces shown. Knowing that wheel A moves to the left with constant velocity of 1.5 m/s determine a) the angular velocity of the rod b) the velocity of the end B of the rod.Solution:

Set up the relative motion equation:

i:

j:

then

and

EGR 232 Lecture 23 Homework Fall 2013Chap. 15, Problem 43Rod AB moves over a small wheel at C while end A moves to the right with a constant velocity of 500 mm/s. At the instant shown, determine a) the angular velocity of the rod. b) the velocity of end B of the rod.Solution:

Relative motion equation:

Separate out the vector equations:

i:

j:

then

To find the velocity of B:

200

140244.13400

θ θ

EGR 232 Lecture 23 Homework Fall 2013Chap. 15, Problem 50Gear A rotates with an angular velocity of 120 rpm clockwise. Knowing that the angular velocity of arm AB is 90 rpm clockwise, determine the corresponding angular velocity of gear B.-----------------------------------------------------Solution:vA=0ωA=120 rpm clockwise = 4π rad/sωAB=90 rpm clockwise = 3π rad/sωB = ?

for rigid body Gear A:

For link AB:

For Gear B:

x

y

D

Equating the two equation for velocity of B.

or 70 rpm clockwise.

EGR 232 Lecture 23 Homework Fall 2013Chap. 15, Problem 55Knowing that crank AB has a constant angular velocity of 160 rpm counterclockwise, determine the angular velocity of rod BD and the velocity of collar D when a) θ = 0, b) θ =90 deg

---------------------------------------------------------

Solution:ωAB=160 rpm CCW = 16.76 rad/s-------------------------------------------------for 0 degrees:

For Link AB:

For Link BD:

therefore:

D

i: j:

--------------------------------------------------------------------------

For angle of 90 degrees:

For Link AB:

For Link BD:

then:

i: j: