Example 4

A cam system is shown in the figure, in which the cam rotates with a clockwise angular velocity of at the instant  . The surface of the cam has a shape of a limacon defined by . Determine the distribution of the velocity of the follower rod AB. If the allowable velocity of AB is , find the probability of failure of the system.

Solution:

The velocity of rod AB is calculated 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.