LIU
Solved problems
Chapter 8
Mechanical systems II
Problem 1
The cam-follower, shown in the figure below, is to be used for a platform that will repeatedly lift
boxes from a lower conveyor to an upper conveyor. The prescribed follower motion for this
application is as follow:
1. Rise 2 in. in 1.2 s using constant velocity
2. Dwell for 0.3 s.
3. Fall 1 in. in 0.9 s using the cycloidal fall motion scheme.
4. Dwell 0.6 s.
5. Fall 1 in. in 0.9 s using the cycloidal fall motion scheme.
a) Calculate the time to complete full cycle and required rotational constant speed
of the cam.
b) Determine the cam angle of rotation for each follower motion interval
c) Fill the table below that tabulates follower displacement versus time and cam
rotation.
For a cycloidal fall, Interval 3, the displacement equation is given as:
*
(
)
(
)+ where h = 2 in, T1 = 0.9 s for 1.5  t  2.4 s
For a cycloidal fall, Interval 5, the displacement equation is given as:
*
(
)
(
)+ where h = 1 in, T2 = 0.9 s for 3  t  3.9 s
Time (s) Cam Angle (degree) Follower Displacement (inches)
0
0.2
0.5
0.8
1
1.2
1.5
1.8
2
2.2
2.4
2.8
3
3.2
3.4
3.9
Solution
Problem 2
A Double Dwell Cam is designed to move a follower as follow:
1. Rise to 5 inches, in 90°, using a polynomial function
2. Dwell for 100°,
3. Fall 5 inches in 90°, using a polynomial function
4. Dwell for the remainder.
Design the Cam by finding the SVAJ Curves for the total cycle.

The displacement polynomial function for the rise is given as:
( )

( )
( )
The displacement polynomial function for the fall is given as:
( )
( )
( )
( )