# Finding an angle

#### Joan

Hi all,

I'm working in a machine that has 3 measuring devices.

Those measuring devices measure distance.

Mechanically it's impossible to mount them perfectly aligned therefore I don't know the position nor the angle the 3 measuring devices are mounted.

The machine must measure the circumference radius of the introduced part.

I have 3 master circumference parts with a known radius each.

All circumferences (parts) are always mounted in the same position.

I know that the perfect difference between master circumference 1 and master circumference 2 is the difference between their radius:

r1 - r2 = perfect distance between circumferences.

And I can measure the first one m1 and the second one m2 and therefore I can get the distance of the two contact points with each circumference.

The problem is that I don't know the angle, neither the position of the measuring device and I need to find that to be able to use the feedback from the sensor to find out the circumference radius.

Is it possible to find this data? And which would be the right approach?

A link to a small diagram to make this a little bit clearer:

Joan.

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#### romsek

Math Team
Are you talking about just calibrating the machine before use by finding these angles?
Using your known set of master disks it's possible to generate a calibration curve for the measured distance between disk edges and the angle of the sensor.

I've done it for master disks of 3 and 4 units. The distance vs angle is roughly parabolic. Do you have any idea just how far off horizontal or vertical these sensors might be?
The tighter that range the better simple models fit.

Anyway, it's a simple enough matter to then slot in your disks and measure the distance and get a pretty good estimate of the angle the sensor if off horizontal or vertical by.

Then knowing that you can calibrate the single measured distance of the unknown disks to the actual circumference of them.

Does that sound like what you want to do?

#### Joan

Yes romsek, that sounds exactly what I want to do. but I have no idea on how to proceed...

The sensors will be at 10mm from the part while the part is loaded into the machine.
After loading the part, the sensors will have to measure the part with a maximum error of 30 micrometers.

Remember I don't know where the sensor is: position nor orientation.

THANK YOU VERY MUCH for your time and help!

#### romsek

Math Team
Yes romsek, that sounds exactly what I want to do. but I have no idea on how to proceed...

The sensors will be at 10mm from the part while the part is loaded into the machine.
After loading the part, the sensors will have to measure the part with a maximum error of 30 micrometers.

Remember I don't know where the sensor is: position nor orientation.

THANK YOU VERY MUCH for your time and help!
What are the sizes of your master disks? What software do you have available to you?
Do you have any limits on the positional and angular deviations?

#### Joan

Good morning romsek,

Master disks are 55.030 mm, 55.015 mm and 55.000 mm.
I don't have limits, but the physical position of the sensors must be quite similar to the perfect position.
In fact the error should be only the capacity of the mechanical engineers to place the sensors in the right positions (mechanical error due to the bolting, mechanical error induced by the machining, mechanical error due to various physical factors).

Thank you again!

#### romsek

Math Team
Do you have any information on the precision and accuracy of the distance measurements your system is making?
It could well be that the raw sensor data has more error in it than any angular misalignment causes.

#### Joan

The sensor is certified and calibrated to give 1 micro meter precision in 10 mm detection range.

#### romsek

Math Team
ok, give me a few days to work this up

#### Joan

WOW! THANK YOU VERY MUCH for spending time on that.

#### romsek

Math Team
The sensors will be at 10mm from the part while the part is loaded into the machine.
After loading the part, the sensors will have to measure the part with a maximum error of 30 micrometers.
I'm confused by this a bit. I assume different sized parts are loaded into the machine. Does this mean that the sensor position moves until it thinks it's 10mm from the part?
This can't be true or you would have mentioned it. What does the first sentence above mean?

Also what software do you have available to you? I work in Mathematica. If you want to generate tables on your own, which I hope you do.
You're going to either need to have access to that, or to be able to translate the routines into what you do have access to.

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