Example 6
A cam system is shown in the figure, in which the cam rotates
with a clockwise angular velocity of 
at the instant 
. The angular acceleration
of the cam follows a normal distribution of 
. The surface of the cam has a shape
of a limacon defined by 
. Determine the distribution of 
, which is the acceleration
of the follower rod AB. If the allowable acceleration is 
, the system
fails when the magnitude of is larger than that of 
. Find the
probability of failure of the system.
Solution:
At the instant , we have
The time derivatives are calculated by
The acceleration of rod AB is given by
Since , also follows a normal distribution
with
Let 
, the mean and standard deviation of
are then
given by
Thus, the probability of failure of the cam system is given by
Ans.