Offset Circle Equation: Determining Radius from Angle of Rotation

[dwepplo]

Hi,

I’m trying to write a probing cycle on a CNC for calibrating from a standard.

I have a circle with a known diameter but it is not located on the center of rotation – the center of rotation is X/Y intercept.

The center of rotation will always lie within the circle.

I’m trying to write a function that describes the radius in terms of angle of rotation (A) – B is the center of known circle. I can only measure by rotating and I won’t know the distance from the axis – only the change in radius versus the angle of rotation.

This is what I’m planning:

I have to first find the coordinates of the center of the circle by rotating and measuring then use this data in the function for describing the radius.

Is this the best approach?

What is the approach for finding the center of the circle?

To describe the radius would I use polar coordinates, if so what does a shifted polar eqn look like?

It’s been a while since I’ve thought about some of these things and I’m hoping someone can point me in the right direction.

Thank you,

Dan

 

[jvicens]

Hi Dan,

Thank you for your question. Your approach to first finding the coordinates of the center of the circle by rotating and measuring is a good starting point. However, there are a few other considerations you may want to take into account.

One approach for finding the center of the circle could be to use a combination of measurements and calculations. You could measure the radius of the circle at multiple angles and then use those measurements to calculate the coordinates of the center using trigonometric functions. Alternatively, you could use a coordinate measuring machine (CMM) to directly measure the coordinates of the center.

To describe the radius in terms of the angle of rotation, you could use polar coordinates as you suggested. A shifted polar equation would look like r = f(θ) + c, where r is the radius, θ is the angle of rotation, f(θ) is the function describing the radius, and c is a constant representing the shift from the center of rotation.

Another approach you could consider is using a least squares regression to fit a curve to your measured data points, which would give you an equation describing the radius in terms of the angle of rotation. This method may be more accurate and efficient, especially if you have a lot of data points.

I hope this helps guide you in the right direction. Best of luck with your probing cycle!