Please help about Delta arms length and width

Hi everyone. I am building this machine:
[www.thingiverse.com]
and I want to find an effector suitable for this design which have nozzle cooling fan, e3d cooling fan and with an auto probe function. There are plenty of designs on the internet but I couldn't find any information about a point about the arms. Should the arm widths on the carriage side and on the effector side be the same size? On the original design, the arm width is 50mm. But when I find a design, I measure the width but mostly they don't be the same.
Also another question is about the arm lengths. I read about the 80% rule and the reference length is the distance between towers. But in the design above, the carriages move along the smooth rods, not on the aluminum extrusions. So the rule about "distance between towers" should be "distance between the smooth rods", am I right?

I can't imagine an 80% rule that would be anywhere close to correct. The print bed can be totally enclosed between the towers/horizontals or extend outside the horizontals. The rule which gives the best compromise between speed and accuracy is the 60/20 degree rule. It says when the effector is centered the arms should be at or near 60 degrees. 20 degrees should be the maximum.

Each set of arms must be parallel within a small fraction of a millimeter. The further apart the arms, the more rigid the machine but the print area decreases.

The Duet3D effector [www.duet3d.com] meets that specification although you have to print the print cooling fan duct yourself. It's designed to be used with magnetic rods and ball studs, with the rods spaced 55 mm apart.

Regarding geometry, see the reply from effrench.

Edited 2 time(s). Last edit at 08/20/2017 06:20PM by dc42.

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Large delta printer [miscsolutions.wordpress.com], E3D tool changer, Robotdigg SCARA printer, Crane Quad and Ormerod

Disclosure: I design Duet electronics and work on RepRapFirmware, [duet3d.com].

You could try [www.thingiverse.com] -- this is configurable regarding distance apart of the rods. It is designed for mechanical rod-ends as per your "Kossel Alt" design, and includes fan mounts (although the author says they work but he's not happy with them. It also apparently includes a mount for a bltouch probe.

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etfrench
The further apart the arms, the more rigid the machine but the print area decreases.

I'm struggling to see how increasing arm width reduces print area... is that just due to the fact that wide arms requires a large effector, which in turn means the nozzle itself can't go near to the base of each tower? Or is there more to it than that?

Also, if you increase the arm length, you will get a larger, more triangular, print area with apexes out between the towers? But as a consequence lose some height?

So longer arms would compensate for wider apart, at the cost of some height? Whereas shorter arms, close together. would result in a rounder print area? Presumably there's some optimum ratio of arm length to arm width? And arm length is proportional to tower spacing, based on the 60/20 rule?

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frankvdh

Quote
etfrench
The further apart the arms, the more rigid the machine but the print area decreases.

I'm struggling to see how increasing arm width reduces print area... is that just due to the fact that wide arms requires a large effector, which in turn means the nozzle itself can't go near to the base of each tower? Or is there more to it than that?

Also, if you increase the arm length, you will get a larger, more triangular, print area with apexes out between the towers? But as a consequence lose some height?

So longer arms would compensate for wider apart, at the cost of some height? Whereas shorter arms, close together. would result in a rounder print area? Presumably there's some optimum ratio of arm length to arm width? And arm length is proportional to tower spacing, based on the 60/20 rule?

Yes, the larger effector means it will run into the towers/belts sooner and the center will further from the towers.
I don't know if there is an optimum ratio for arm length to width. I'm using 375mm long by 60mm wide arms with a built area >300mm diameter and 290mm high.
There are a couple of delta simulators available that will show the effects of changing the arm length and width.

OK. Based on the rules mentioned above and also to my old geometry knowledge, here is my calculation:
If we accept the 20-60 is not a theory, it is a rule so I will stick with it after now. I have manually assembled the rod ends to the ball links and measured a maximum angle of around 30 degree between them. So we can move the arm to a maximum of 30 degree. This is illustrated with blue lines in the attached picture. Our effector's center ( so the nozzle) will be on this 30 degree line. Also my carriages have 22mm offset from the vertical steel rods' centers and my effector has 21.5mm offset. The distance from the carriage's ball links center axis to the middle of the line 6 in the picture is 295mm. (Line 6 is the reference line extending from one of the the middle of two ball links of same carriage to the other). So after subtracting the offsets: 295-21.5-22=251.5mm . This should be the horizontal distance of my triangle.

Here is the calculation. I have taken the 22 degree instead of 20 degree just in case. According to the calculations, my arm length should be ~271mm.

Maybe my calculations can be wrong but this is the way I did this. Thank you very much to all who gave me the valuable answers above.

Edited 1 time(s). Last edit at 08/23/2017 07:37AM by s3rkan.

Your diagram should be a Reuleaux Triangle to be more accurate.
I'd post an image, but Photobucket is holding my photos for ransom

Basically, draw an arc from each arm on the effector when it's at 90 degrees (in front of the tower). The radius of the arc is the position of that arm on the effector when it's at the maximum extension (20 degrees). Repeat for the other arm. Locate the effector so the center of the arms is on each of those arcs. This will give you the maximum print area at the bed. It will decrease as you move off of the bed.

Note: It is possible to design a (working) delta where the angle in front of the towers is >90 degrees.

Quote
etfrench
Your diagram should be a Reuleaux Triangle to be more accurate.
I'd post an image, but Photobucket is holding my photos for ransom

Basically, draw an arc from each arm on the effector when it's at 90 degrees (in front of the tower). The radius of the arc is the position of that arm on the effector when it's at the maximum extension (20 degrees). Repeat for the other arm. Locate the effector so the center of the arms is on each of those arcs. This will give you the maximum print area at the bed. It will decrease as you move off of the bed.

Note: It is possible to design a (working) delta where the angle in front of the towers is >90 degrees.

Thank you for the tips, but I couldn't visualize what you meant, sorry my bad Is there any website containing the relevant picture?

Put the effector directly in front of a tower. The right triangle formed by the arms at this position and at 20 degrees will give you the length of the arc that will contain the maximum travel for that arm. Repeat for the other 5 arms.

There are one or more OpenScad delta simultators available. It shouldn't be too hard to find one.