How long are the carbon fibre rods for a Travelling Kossel?

Question

TL;DR - For a given Kossel frame size (w.r.t. the vertical and horizontal frame lengths of the aluminium extrusion), what would the length of the carbon fibre rods be?

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A case in point, from RepRapWiki - Kossel, there is an intriguing note about a scaled down Kossel:

Optionally scale down to a Traveling RepRap that fits within IATA hand luggage size limit (see transportation):

• Frame height: 550 mm.
• Footprint: triangle, 270 mm width, 250 mm across (210 mm 15 x 15 mm aluminium extrusion like OpenBeam + printed corners).

However, there is no mention of the length of the carbon fibre rods (carbon tubes).

Now, as per my previous question, For a larger build volume, what lengths of 2020 aluminium do I need?, is there a formula or ratio by which one needs to abide? Whereas in my previous question, the answer was along the lines of: Not really, you can use any lengths, within reason, and account for it later in the firmware, I would imagine that the Delta aspect of the printer is somewhat more exacting.

I have tried googling for further information on this Travelling Kossel, but found nothing, except for the information of RepRapWiki.

Looking at the corresponding lengths (vertical/horizontal) of the aluminium versus those of the carbon fibre rods for the Mini and XL:

• 600/240 mm versus 180 mm
• 750/360 mm versus 300 mm

I really can not see what the (trigonometric) relationship is, and therefore can not deduce the lengths of the carbon rods for the Travelling Kossel.

Unless it is simply that the carbon rods are 60 mm shorter than the aluminium horizontals? Is it really as simple as that, or is this just a coincidence? In which case, would the carbon rods be (210 - 60 =) 150 mm?

By extension, imagine if you wanted to build a Kossel XXXL, with a horizontal aluminium extrusion length of, let's say, 1000 mm, would the length of the carbon rods be 940 mm?

Any ideas?

Answer 1

Most information I was able to find was the arms are 80% the length of the horizontal structure. I did find a copy of the original Google Sheets that everyone used a few years ago here. The source of that link did mention that there may have been some issues with it but all of those links were dead ends.

Some things to note:

The height doesn't matter, it has no relationship with the arms other than you are losing approximately the arm length from the height when figuring print area as some arms will approach vertical when reaching the outsides of your print area.

The arm length isn't terribly important from what I could find. Longer arms = less travel of the carriages and possibly lower resolution. Shorter arms = more travel of the carriages and possibly lower print speed due to required movement.

Answer 2

To compliment tjb1's answer, The link seems to go to a spreadsheet that doesn't have any formulae in it. However, I managed to find a copy, from Google groups: How to calculate Delta Dimensions for new build.

However, another source of the Document is Kossel frame calculator ([email protected]). Right at the top is a posting of Johan's (who is the designer of the Kossel) spreadsheet, which is essentially the same as before, but it is contained within an interesting message thread.

There are a few more calculators, that a quick google search will throw up, which I have listed in a short blog, Kossel - The Ratio:

• Delta Frame Calculator | OpenBuilds

• KosselPrinter/Kossel frame calculator.xlsx at master · aleung … – GitHub

• Kossel frame calculator – Google Groups

• Calculations | Pearltrees

I have an enhanced version that allows additional parameters to be modified, see Github: Greenonline/Kossel/Spreadsheets.

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Design Process by David Crocker

Apparently, the ratio is not particularly vital. I found a design process in the comments section of More upgrades to the large Delta 3D printer:

The design process goes something like this:

1. Estimate the size of effector you will need.
2. Given that effector size, work out how close to the towers the nozzle will be able to get. From that and the desired printing radius, work out what radius the towers are on.
3. That fixes the lengths of the horizontal extrusions. Choose the diagonal rod length so that when at the edge of the bed opposite a tower, the rods to that tower are at 20 degrees or a little more to the horizontal.
4. Given that diagonal rod length, choose the rod separation. I suggest about 1/6 of the rod length (this is larger than on my delta).
5. If that rod separation means you need a larger effector, repeat from step 1.
6. Choose the tower height to give the required print height at the edges of the bed, when one pair of rods may be more or less vertical.

When I queried David about his use of the 0.8 ratio, again in the comments section, on Building a large delta 3D printer, this was his reply:

The notion that there is a single ratio of diagonal rod to horizontal extrusion length that is right for all delta printers is misguided. It depends on the geometry of the corners that join the horizontals to the towers, the size of the effector, and the carriage design. What matters is that the rods are at no less than 20 degrees (preferably 25 or more) to the horizontal when the nozzle is at the edge of the bed opposite a tower.