# Calc uncertainty of angle; by measuring x,y points

#### greif

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I am setting up a method to measure angles in an x,y plane using a CMM. I have applied the CMM linear error to the endpoint of the shortest leg (to cover worst case), then compared the resulting angles to the same leg with no error applied. The difference between these two angles gives me a k=2 uncertainty line item to use in the overall angular uncertainty. I also applied the resolution of the CMM to a small angle and compared the difference to come up with an angular resolution to use as a line item in the uncertainty calculation.

Question:
1) Since two lines are needed to form an angle, it appears that I need to have a line item of CMM caused angular error (due to CMM x,y uncertainty) for both Line 1 and Line 2 ( since each line is an independent measurement). Is this sound reasoning?
2) For uncertainty angular resolution; do I also need to have this in as two line items? (one for Line 1 and one for line 2) Or is angular resolution covered as a whole?

Example:
Line 1 points ; 0,0 5,0
Line 2 Points: 0,0, 2,2

Angular resolution, with CMM of 0.002mm resolution= 0.0405 degrees
k=1 uncertainty of the CMM component due to short leg (Line 2) = 0.0333 degrees
k=1 uncertainty of the CMM component due to long leg (Line 1) = 0.0134 degrees

Uncertainty calc line items:
1) Uncert due to CMM, Line 1: 0.0333 distribution, normal
2) Uncert due to CMM, Line 2: 0.0134 distribution, normal
3) Uncert due to angular res.: 0.0405 distribution, rect x 2

Resulting k=2 uncertainty of above is 0.076 degrees.

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