Ring Kit Rotational Radius

Wiki summary:

On the ring kit, the rotation radius is calculated to be 138.14 mm. This value has been used in at least one successful MaslowCNC high accuracy setup.

The rest of this topic explains how it was calculated:

@madgrizzle said:

I calculate the rotational radius of the ring kit to be ~139.82 mm +/- some very small amount…This is how I calculated it and would love someone to check my work. I based it off the drawings and the measurement @bar provided for the bearings in another thread (I assume the inner radius is 13 mm)

The premise is that the zero point is not the end of the first link, but rather the midpoint of the first link. Therefore, we need to calculate the distance from the center of the router bit to the midpoint of the first link. Furthermore, it’s assumed the cotter pin is very close to the same size of the gap between the chain link roller bearings and therefore the center of the cotter pin is practically at the zero point. The drawing below is not to scale.



the cotter pin is nowhere close to the full gap in the chain.

from this link: https://www.usarollerchain.com/roller-chain-size-chart-s/4869.htm

spacing between pins is .25"(6.35mm) the rollers are .13"(3.3mm) (half of each roller is between the pins), so the gap between rollers is .12"(3mm), I’m pretty sure that the cotter pins are thinner than that)

also, the distance from the centers of the bearings to the edge of the ring is a little more than you are calculating (the ring isn’t a stright line, so the curve moves things away,

these aren’t huge errors, I would guess you are within a mm or so

My ring kit was missing the cotter pins so I don’t know what was shipped (I had cotter pins already though so no big deal). I went by what was found on a thread with BOM… https://www.fastenal.com/products/details/45287. This showed the diameter as 0.093" or 2.36 mm.

I realize I had measured the gap between rollers and didn’t consider there was no roller at the very end… so that adds a little more gap. Let’s say its 3.2mm and assume the zero point is still the center of the last link regardless of whether there’s a roller on the end or not. So the zero point is about 0.42 mm out further from that… so add that to the rotational radius… call it 140.24 mm (139.82+0.42)


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why are you using the master link rather than just going through the regular link (that will make a mm or so difference between people doing each approach)

I’m not, that’s just the diagram I pulled from the web. Nevertheless, there’s no roller bearing on the last link, just the pin.

I did another drawing that was to scale and then measured it. I get a rotational radius of 139.1 mm doing it this way. It can be off a very small amount based upon the diameter of the hairpin cotter pin. The diameters of the bearing is based upon @bar’s measurements from this post:



I was just looking at this math. I believe there is one mistake. I don’t know how significant it will be. The rollers are not in-line with the chain and the router bit, so it is not a simple subtraction of 105-13 mm. Three points make a triangle: the point where the roller bearing touches the inside edge of the ring, the center of the router bit, and the center-point between the two rollers. Here is the math.

New variable: Distance between roller-centers (I don’t know the exact number, but I will estimate at 35 mm for now)

New variable: Distance from inside edge of ring to center-point between rollers. Use Pythagorean theorem.
= sqrt((105-13)^2-(32/2)^2) = 90.598

Now, the math looks like this:

90.598 mm distance from center of router bit center between bearings
+50.5 mm center between bearings to outside edge of carriage
141.098 mm distance from center of router bit to outside edge of carriage
-1.5 thickness of carriage
-1.18 mm radius of cotter pin
138.418 mm distance from center of router bit to chain zer point (i.e., rotational radius)

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you don’t need to do all this math.

the rotation radius is the distance from the bit to the point on the chain that was at 12 o’clock when you started feeding chain out (the middle of the first link, even though we now say to put the pin through the second link)

so you don’t have to do all that math (and if you try to do the math that way, the radius of the ring needs to show up there somewhere)

but if you are correct, the actual rotation radius needs to be reduced by 6.35mm due to connecting to the second link.

Also, you don’t subtract the radius of the cotter pin unless it completely fills the gap in the link (and I’m pretty sure it doesn’t come close to that)

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It is the same calculation as @madgrizzle’s above, in post 1. It may not be as clear as I had intended, but my calculations start at @madgrizzle’s line 3. The difference is the calculation of the “distance from center of router bit to center of *”. @madgrizzle calculates the distance from the bit-center to one bearing-center, whereas I calculate the distance from the bit-center to the mid-point between the two bearings. I believe this is a better number. The difference is only about 2 mm.



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Good catch @Joshua. So is everyone in agreement 138.14 is the canonical best value we have for ring rotation radius right now?


I made a WAG on the 35 mm number, which is the distance between the bearings. Just to be rigorous, could someone confirm what this measurement should be?


Not bad - I measure 32mm center-to-center.

Hello, i am having some problems while cutting.
I make a ring at home, but the radious isnt the one yuo talk here, maybe (i dont remember) is 110 mm, the distance to de pin are others…i ask you, i have to rebuildit with de dimennssions you said on this post? Are they hard coded?
I hope no…

No, you can change the rotation radius in the settings. You want the distance from the end of the chain to the center of the rotation.

actually, it’s the distance from the point in the chain that straddles the pin
when the sprocket is at 12 o’clock to the center of the bit.

David Lang

@Mario_Giacummo , Yes, I’m all over the Forum :grin:
How is the chain connected here? If this is a free rotating tube, you would measure from the centre of the screw. If it is a fixed tube, from the first pin on the chain that can move freely.
Are you asking because of the zig-zag cuts?

:slight_smile: i am asking from allll

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Its a little hook…
But this dont have nothing to fo about the zig zag…i guess