Finding PDF of Link B for 2-Bar Linkage

[MO53]

Any help is appreciated on this:

This is the projection on the x-axis of a 2-bar linkage. I need to find the PDF of the end of the second link (point B)

1. Link C of length rC is pinned at the origin and its other end is pinned to link B at point C. Its length projected on the x-axis is nomally distributed with mean μC=0 and std dev σC = 0.000375.

2. Link B of length r.B is pinned at point C on link C and its other end is point B. Its length projected on the x-axis is nomally distributed with mean μB= xC (I think) and std dev σB = 0.00125.

I need to find the PDF for point B as a function of x.

 

[uart]

Hi MOD53. Do you need to find the PDF of point B or do you just need to find the PDF of the projection of point B onto the x axis?

 

[MO53]

Thanks for responding. I would settle for the projection, just to understand the problem better. I am trying to decide if the convolution integral is the right solution to this part of the problem.

This is part of a larger problem, listed below.

Find the percentage of the population where the distance from point A to point B is greater than 0.010 inch.

Where:
rA, rB and rC are a normally distributed link lengths of σA=.00175 σB= .000375 σC=.00125 inch.

Think of the hands of a clock. Hand A is fixed at 3 oclock and its length is a normal distribution. Point A is at the end of the hand.

Hand BC is jointed. The joint is point C, at nomally distributed radius C from clock center. The tip of the hand is point B, at the end of radius B which is normally distributed and pinned at C. The angles of C and B are both uniformly distributed from the x-axis (both angles are equally likely to be anything from 0 to 360 degrees).

What percentage of the time are the ends of the hands more than 0.010 inch from each other?

 

[MO53]

BTW, this is not homework, its a tolerance analysis for a medical product. Can you suggest the best place to post this?