Help please, I need to visualise Celtic knot diameters

[AndyP]

You folks have seen how 4 veneers precisely angled into a square blank can create a Celtic knot design in a pen

Celtic Knot Pen WIP

This is how I do it. probably how everyone else does it too :) Although the clamping jig is 100% my idea. Each pen is made up of two perfectly square, in cross section, pieces of wood (blanks) each about 2.5 inches long. Having decided where on the pen the knot should go, in this case near...

www.thewoodhaven2.co.uk

I have only ever done this on a ¾” square pen blank.

Supposing I started with a 2.5” square blank with the 4 angled inserts at 45 ° at what diameter will the complete knot appear? Can this be calculated ?

 

[Robert]

Wouldn't it just be in the same ratio of starting square size to final round diameter?

So (say) 25:16 ratio for a pen in mm would be 63/25 x 16 = 34mm dia..

 

[Woodbloke]

You folks have seen how 4 veneers precisely angled into a square blank can create a Celtic knot design in a pen

Celtic Knot Pen WIP

This is how I do it. probably how everyone else does it too :) Although the clamping jig is 100% my idea. Each pen is made up of two perfectly square, in cross section, pieces of wood (blanks) each about 2.5 inches long. Having decided where on the pen the knot should go, in this case near...

www.thewoodhaven2.co.uk

I have only ever done this on a ¾” square pen blank.

I still haven't used the one you made for me Andy; will probably buy a decent kit for from somewhere like Beaufort lnk, who now are stocked by Yandles - Rob

 

[AndyP]

Wouldn't it just be in the same ratio of starting square size to final round diameter?

So (say) 25:16 ratio for a pen in mm would be 63/25 x 16 = 34mm dia..

I don’t thick so Robert, the complete knot on the pen appears before the final diameter is reached. I think the only way I can satisfy myself is make a test piece which is a pain as it’s a 4 day job, although if I use just two inserts opposite each other it may do.
A surprise event has just been brought to my attention and I now need to make a suitable gift before the end of April.

 

[Lons]

I don't know the answer Andy but you might get it from one of the guys on https://penturners.co.uk/ if you ask the question

 

[Dr.Al]

I don't think it matters. Having read the question, I had no idea, so I decided to cheat and let Solidworks do the work.

This is a 19 mm blank, with 0.6 mm veneers, turned down to 19 mm final diameter:



This is the same blank turned down to 8 mm diameter:



If we start with a 63.5 mm blank (ah, the joys of parametric CAD!) and turn it down to a 63.5 mm diameter (still sticking with 0.6 mm veneers), it looks like this:



40 mm final size:



20 mm final size:



I'll save the CAD model, so if you want me to stick any other numbers in for blank size, veneer thickness and final diameter, then let me know.

 

[AndyP]

Brilliant Al, thank you so much my fears are allayed. I’ve no idea what parametric CAD is but your use of it has earned you a virtual beer or two.
I want to incorporate the knots in a couple of pepper & salt grinders and having never turned a knot in anything with a diameter greater than an 1” I just could not visualise how they would come out.
I’ll not be getting my kits until 5th April when daughter returns for easter break and I need to have the mills made by the 18th so I will not have much time to practice.

 

[Dr.Al]

No problem: it didn't take long.

Parametric CAD is how most professional 3D CAD programmes work (but not things like SketchUp, Tinkercad et al). It means you can drive the design by dimensions & can, if you want, even have a spreadsheet controlling the design so you stick a new row in the spreadsheet and a new part magically appears.

Imagine you were modelling an M6, 1mm pitch, 20mm screw. With parametric CAD, you'd set the diameter, pitch, length and hex socket size as parameters as you drew that one screw. Then you could point it at a spreadsheet & produce CAD models of every screw from M0.5 up to M64, every pitch & every length, without having to do any drawing work.