Example 5

The surface of a cam is expressed by a logarithmic spiral formula , where  is in radians. The cam rotates at an angular velocity of . Determine the distribution of the velocity of the follower rod AB at the instant . If the allowable velocity of AB is , find the probability of failure of the system.

Solution:

The velocity of rod AB is calculated by

in which 

Thus,  could be rewritten as

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.