# Finding the radius of an arc — from bent component to flat

I am designing a table that has a leg bent at about 100º. This component has an arc cut on its face at the point that it bends. But before I do that I need to find the radius of the arc in the flat board. I will cut the arc on a CNC and bend that component.

Is there a way I can find the radius of the arc before it is bent?

@jeremyp
There is a _Radius command that will tell you the exact value, if you need the center just turn the Center Osnap on and create a point on it…
Does that help?

I’m not sure that helps. I will draw the bent component on paper and in Rhino but the radius of that arc will change from a flat board to a bent one. Is there a way to unbend (for lack of a better word) a component in Rhino and measure the new (larger) radius of that arc. Or another way to do it?

It’s a different way of working for me — I am drawing the final (bent) form but I need to work with flat timber first.

UnRoll is the command you are looking for. It will unroll a developable surface which has one set of isolines straight. Also the surface can’t be twisted (such as a helix). http://www.rhino3.de/design/modeling/developable/

I tried UnrollSrf but I’m not sure that works as required. It unrolls the arc flat so there is no radius to measure.

Is there another way to do this without flattening the geomtery?

Based on the image you posted, you have a different situation than I previously thought. How will the part be physically made? Do you want to cut a groove across a flat part and then then fold the part at the groove?

It will be steam bent. The internal arc is to help the component bend without compressing the fibres.

Because of behavior of wood when it is being steam bent there is no simple way to relate the final shape of the arc to the shape before bending.

That’s not really relevant. Rhino is a design tool that is used to make furniture that is always moving in one way or another. I know the radius in Rhino is not going to be exactly what it is in the final piece.

from this view, it looks like that curve isn’t a radius. (but if it is, you could use the Radius command to find out the dimension as Rodri suggested)
can you post the .3DM?

actually, I’m pretty sure I don’t quite understand what you’re after.

Actually it is very relevant if I understand your question correctly. You want the shape of a piece of wood needed before steam bending so that it will have the desired shape with an arc of the required radius after steam bending. That depends on the behavior of the piece of wood when it is steam bent. The behavior of wood when steam bent is more complicated than it might appear to most observers, and the behavior around a groove is particularly complicated. To answer your question a sophisticated analysis tool such as non-linear finite element software and a good understanding of the physics of steam bending wood are required. Rhino is not such a tool.

Rhino is used to design the geometry of furniture. However there is nothing inherent in Rhino which accounts for the movement of the furniture - that must be done by the designer based on the designer’s knowledge and experience (or by the builder with suitable modifications to the design).

It took me a little while to understand what you want to do. I think that you have to approach this in an old school fashion.

1. First, bisect the arc on the bent piece.
2. Next, cut the piece on the bisect. Depending on your geometry, you could probably just use split. You may have to extrude the bisect line to make a cutting object.
3. Now, lay the cut pieces flat, the way that they will exist before bending, with the arc halves facing up.

The depth of the cut will be unchanged. The width of the cut, however, will have grown larger. What you will now have is 2 dimensions; the depth and the width. This is no longer describing a circular arc; instead, it is a portion of ellipse or an elliptical arc.
(In the old days, we would have done just what I have described using a paper layout.)

1. Build a rectangle that is the width of your cut and twice as high as your depth. The lower edge of the rectangle and the lowest point on the cut should align.

2. Draw an ellipse, using the corner method, inside the rectangle. The lower half of the ellipse is your new cutting profile.

This assumes that your wood is “perfect”, meaning that it is not going to swell and shrink unevenly. Of course, nature does not behave perfectly just for our convenience, so you may have some small discrepancies in the final part.

Let us know how it works out.

I am a furniture maker. I understand behavior of the wood is not completely predictable. I am not after a precise real-world radius. Ballpark is fine. I know it will be different when I make the piece. (I’ve edited the previous post to reflect that the radius will not be precise — was a typo.

Untitled.3dm (96.3 KB)

There is a flat in the middle of the arc — the radius either side is 18mm.

I’ve laid out roughly what I’m after in the file. The radius of the arcs in the “unbent” component are what I’m trying to find. I’ve just drawn them here to illustrate what I’m trying to measure.

hmm, i don’t think the unbent one will be a radius… or, at least, not if the bent version is a radius.

i see what you’re after now but there’s nothing in rhino that’s going to automatically show you what ‘radius’ to cut into your flat piece.

How do you know the notch in the unbent piece will have the shape you have shown?

How will the sharp angle on the outside of the bent piece be formed?

Since you are a furniture maker have you considered going to the shop and experimenting with steam bending wood with different shape notches?

Thanks Jeff.

it’s possible you could find something useful using the `Bend` command…

that said, rhino’s bend isn’t going to react the same way as a solid piece of wood will (especially with the changing thickness which is occurring in the grooved parts of the wood)… you’d probably have to make a few test pieces, then draw them in rhino, bend the real board and the rhino geometry, then make a comparison between the two results.

upon doing that a few times, you could probably get to the point where you can draw the geometry in rhino and have a pretty good expectation of how the real bend will end up.

an example of Bend:

unbent shape:

during the Bend command (probably use the option ‘Limit to spine’)

result:

regarding the way your original question was posed, that being having the bent object to start with then unbending it, i don’t think there is a way to use `Bend` when the starting Spine is curved (which is what you’d need)… instead, the spine seems to need to be defined as a straight line then you bend that.

@pascal , do you know of a way to use a curved line as the original Spine in the `Bend` command? or must you always define a straight line via two clicked points then proceed to manipulate that straight line?

Bend assumes a straight line to start… Flow might be a workaround.

-Pascal