Finding PDF of Link B for 2-Bar Linkage

In summary, the problem is to find the percentage of the population that falls within a certain tolerance distance from a point.
  • #1
MO53
3
0
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.
 
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  • #2
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?
 
  • #3
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?
 
  • #4
BTW, this is not homework, its a tolerance analysis for a medical product. Can you suggest the best place to post this?
 

What is a 2-Bar Linkage?

A 2-bar linkage is a mechanical linkage that consists of two rigid bars connected by a joint. It is commonly used in machines to transfer motion and force between two points.

Why is it important to find the PDF of Link B for a 2-Bar Linkage?

Finding the PDF (Position Displacement Function) of Link B is important because it allows us to determine the position of Link B in the linkage system. This information is crucial for understanding the overall motion and performance of the 2-bar linkage.

How do you calculate the PDF of Link B for a 2-Bar Linkage?

The PDF of Link B can be calculated using the principle of kinematic analysis, which involves analyzing the motion of the linkage based on its geometry and constraints. The PDF can be determined by solving the equations of the linkage system using trigonometry and geometry.

What factors can affect the PDF of Link B for a 2-Bar Linkage?

The PDF of Link B can be affected by various factors, such as the length and angle of the bars, the position of the joint, and the type of joint used. These factors can alter the geometry and constraints of the linkage system, leading to different PDF values.

What are the practical applications of finding the PDF of Link B for a 2-Bar Linkage?

The PDF of Link B is useful in designing and analyzing 2-bar linkage systems for various applications, including mechanical machines, robotics, and even human and animal movements. It can also aid in troubleshooting and optimizing the performance of existing 2-bar linkage systems.

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