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.