
Hi all,
I need help in a math issue:
Let's say I have 3 measuring devices which give me a distance.
Mechanically those 3 sensors are mounted more or less in the right position, but we can't be sure of the angle neither position the measuring devices are mounted.
I have 3 Mastering parts (3 circumferences of a known radius) that I can mount into the machine at any moment and that I want to use to calibrate the system.
The measuring error of the 3 measuring devices can be dismissed.
this is a small diagram to represent the problem: https://i.stack.imgur.com/a2AyG.png[^]
2 known master circumferences give me a distance [d1] between circumferences (d1 = radius 1  radius 2).
For each circumference the sensor will give me a different measure m1 and m2.
Given the difference between r1r2 and m2m1 could I find the angle in which the measuring device is mounted?
Summarizing:
2 master circumferences mounted in the same center.
3 external measuring devices mounted completely unaligned with the center.
I don't know the measuring devices position.
The red lines in the drawing are the vector lines the measuring device measures would be placed into.
The real measures (in this drawing) would be the distance from the sensor to the position where the red line crosses a circle.
Any help will be welcome...
Thank you all...
modified 3Feb20 10:43am.





Joan M wrote: With 2 circumferences of a known radius I would know the distance between both (Radius 1 [r1] (big)  Radius 2 [r2] (small)). Surely that will depend on where the two devices are situated? Or, are you saying that you know the distance between them? I am having difficulty picturing the actual setup of the devices, and the item they are trying to measure.





The 3 measuring devices are mounted around the circular part.
But I don't know the exact position and orientation of the measuring devices because the mechanical engineers can't guarantee it.
I need to find the position and angle of the 3 measuring devices given the known circular parts and the measures the devices take.
Circular parts are always mounted in the same center position.
modified 3Feb20 6:24am.





Joan M wrote: The 3 measuring devices are mounted around the circular part. What does that mean; the circular part of what? I really think we need a picture.





https://i.stack.imgur.com/a2AyG.png[^]
You are super right, sorry...
You can see more explanations in the original question just under the link itself.
Thanks!
modified 3Feb20 10:44am.





Unless the devices are all measuring to the same known point in the circle you do not have any way of relating the values to each other.





I know it's Monday morning, and I'm still MucusMan: The Human Hagfish but I need a diagram to work out what the heck you are asking about there ...
"I have no idea what I did, but I'm taking full credit for it."  ThisOldTony
AntiTwitter: @DalekDave is now a follower!





https://i.stack.imgur.com/a2AyG.png[^]
2 circumferences mounted in the same center.
3 external measuring devices mounted completely unaligned with the center.
I don't know the measuring devices position.
But I get a distance from the measuring device to the circular master part mounted.
And I have 2 master circular parts.
The red lines in the drawing are the vector lines the measuring device measures would be placed into.
modified 3Feb20 10:44am.






Yes, if I had the xy would be easy, I don't know the position of the measuring device neither the angle it is mounted...





Then I'm not sure what you're asking is possible. you need some way to get 2 points out of this to get an angle. That's the minimum you need (and the 3rd point is implicit)
So your task now is to divine two points. Somehow.
Real programmers use butterflies





yes...





maybe try printing out your drawing and just trying to use a pen to draw the triangles you need. Then see where the points fall. From there, see where the points are in relation to the circles and see if that can't help you. It's a shot in the dark but it's the best i got.
Real programmers use butterflies





What I do not understand is what distances those 3 devices measuring...
What is the significance of endpoint of the red lines in the drawing?
"The only place where Success comes before Work is in the dictionary." Vidal Sassoon, 1928  2012





The measured distances are the length of the red lines when they cross the circles.





Like a beam that hits the surface of the circle and you have the distance without the angle?
"The only place where Success comes before Work is in the dictionary." Vidal Sassoon, 1928  2012





Yes, in that case is a mechanical measuring device, but yes, the red line would represent a beam that measure the distance, but I don't know the incidence angle.
Thank you for spending time on that, I'm sure my super explanations are not making it easy to understand it.





Some observations:
1. Replacing the circle (disk) with an other one will not change the distance the devices measure as long as the circles are on the same plain...
2. There is an option when one or more of the devices will not hit the circle's surface (infinite or error)...
3. There is a whole sphere for each point on the circle's surface that will return the same measurement...
"The only place where Success comes before Work is in the dictionary." Vidal Sassoon, 1928  2012





Yes, yes and yes, but (and I'll write this in the OP) we consider all to be in the same plane.
If it is not... I simply abandon all hope and start crying now...





Even the circle is on a fixed plain and the beams are always hit the surface, you can not know the position of the device as any of the devices can be at any point of a sphere and still return the same distance...
If you would know the distance between the devices it would cut down the possible position to a circle (still a lot but less the a sphere)...
"The only place where Success comes before Work is in the dictionary." Vidal Sassoon, 1928  2012





With no further information I unfortunately think this is a "software can't fix your mechanical problems" situation. I'm not a math wizard though so maybe someone else will chime in.
If there's a way to guarantee a distance between the measurement device and the center of the measured sphere, I think it may be possible. You'd have both sides of the triangle coming out of the measurement device (the "true" distance [distance to center  radius] and the measured) and you could use spherical trigonometry to determine the angle between those sides (the angle of the measurement device) given the difference between the two distances. Honestly that's beyond me though and relies on having perfect spheres. I was never good at trig
EDIT: Also this would in no way let you know where in the xy plane those measurement devices are.





Your question is really unclear, are you trying to calculate d1?
Regardless, if you have neither the positions nor the angles of the devices then you can't get an accurate calculation. Your best option would be to use which ever device gives you the shortest distance, as that will be the most accurate  but certainly cannot guarantee a correct result.
Essentially to get the correct result you need a device pointed directly at the centre point. If they are not pointing directly at the centre point then you could probably compensate for this offset is your calculations, but you would need the angles and positions to be able to do so.





I need to calculate XY position in which the sensor finds the part.
The problem is that the sensor is at an unknown position and angle (which will be very similar to the desired one but I need a really high precision (3 micrometers)).
I only get from the sensor the distance from the sensor to the part.





Joan M wrote: I only get from the sensor the distance from the sensor to the part.
So just to be clear. Do you just get a single value (distance) from the sensor to the outer circle?
Or do you get 2 values, one for outer circle and one for inner circle?





One for each circle.
Thank you for spending time on this. And sorry for my bad explanations, it's difficult for me to describe this clearly in English...



