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# How does the 'radius' value mathematically effect a circular fillet?

Shannon_Kern
Member Posts:

**4**PRO
Hey all. I'm trying to make my model as scalable as possible, and have been having an issue with the fillet function.

I basically have a series of holes drilled into a sheet of metal that is 4.5mm thick. I need to make it into a pillow plate, if that's relevant, and decided the best way to do this was to use the circle fillet function on each of the holes.

This works fine, but I would like to have the fillet

For example, putting a circular fillet on a 2mm extruded hole results in this:

Which is fine, but when I select the outer circle and expect to see a

Which is.. also not the case! I performed all manners of trigonometry from this side view to attempt to figure out where the

So, what exactly is the mathematical relationship between the inputted

I basically have a series of holes drilled into a sheet of metal that is 4.5mm thick. I need to make it into a pillow plate, if that's relevant, and decided the best way to do this was to use the circle fillet function on each of the holes.

This works fine, but I would like to have the fillet

*radius*be directly correlated to the dimensions of the spacing between the holes, and I can't figure out just how the*radius*value of the fillet actually effects the size of the fillet circle.For example, putting a circular fillet on a 2mm extruded hole results in this:

Which is fine, but when I select the outer circle and expect to see a

*radius*of 20mm, I see this instead:**Which.. is not what I expected. I then assumed that the****radius****value was referring to some other radius, like the curve of the circle when facing the filet from the front.**Which is.. also not the case! I performed all manners of trigonometry from this side view to attempt to figure out where the

*20mm radius*value was actually being used, but I can't seem to figure it out. I did check out the fillet class source code, but also couldn't figure out exactly where the radius value was being used.So, what exactly is the mathematical relationship between the inputted

*radius*value for a circular fillet and the actual appearance of that fillet? A simple equation would be very, very helpful & appreciated. Thanks for any help!0

## Comments

1,8084PRO1,8084PROSince there must be a formula *somewhere* that's actually executing, which I do need to get eventually to be able to make this scalable, I was trying to derive the length of the curve mathematically and am a bit confused as to where exactly the

20mm radiusvalue actually comes into play, as the length of the curve in the upper image is~13.554,unless my calculations are completely wrong.Can someone help me out here? I just need a formula that relates the radius to the actual size of the circle produced. I can't seem to find it anywhere. Whether it be in Onshape or on the kernel itself, there's gotta be a formula executing somewhere. Thanks a ton!

787✭✭✭✭821✭✭✭✭Yeah, calculus is definitely not required. Just trig. Here's the math.

θ = asin[(R-Y)/R]

X = R cos θ

Z = D + 2X

Z = D + 2R cos(asin[(R-Y)/R])