How to correctly measure arm length?

With all the threads talking about the to know absolutely to the 1/10 or better of a mm the actual arm length for a Delta printer, I now have a quandary about which measurement is correct.

For Traxxas style joints it seems to be logically simple: Measure the distance from centre of bolt hole to centre of bolt hole.

It seems to become more complex for any joint using a round ball that rides in a socket.
Attached is a very rough drawing of how my arm design is done.

For that sake of easy calculations lets call the distance between the bottom of the ball cups exactly 500mm, the ball cups are 4mm deep and the steel ball on the effector and carriage are 10mm.

So in my case the arm joint revolves around the centre of the 10mm ball so is my arm for the purpose of delta calculations 510mm?

Yep, 510mm.

It's measured from the centre of the ball to the centre of the other ball.

OK, in that case the actual physical arm length is not the number needed. In this case it's the virtual arm length.

And I wonder just how many people this actually trips up.

its nothing virtual.. its how you measure the arm length... its always been a measure pivot to pivot whatever you use magnetic,rc car joint or any others form of joint

Interested to hear how everybody 'accurately' measures the arm length to a 1/10 mm...My arms are ~330mm in length and most of my really accurate equipment is only capable of measuring to 12"/300mm...

Part way through a Kossel XL from Builda3DPrinter so this is about to become a critical issue!

Simon

Use the jig in which you built your arms. Drive a nail into the center of the jig. Measure from the sides of the arm to the nail. Measure the nail thickness and thickness of the screws at the ends. Compute the real length from the measurements.

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Simon0362
Interested to hear how everybody 'accurately' measures the arm length to a 1/10 mm...My arms are ~330mm in length and most of my really accurate equipment is only capable of measuring to 12"/300mm...

Part way through a Kossel XL from Builda3DPrinter so this is about to become a critical issue!

Simon

I wire cut a gauge for mine. The two measurement faces are about as parallel as machined faces are going to get. I built in adjustments to the arms and then set them to the jig. It would be the same principle as setting a mic to a dimension and adjusting the rod to fit. For this type of jig the faces need to be very parallel which is not easy to achieve with hand tools. After setting with this jig which I keep at home with my machine I checked a few with a mic (we have mic' sat work out to about a meter) and they were within a few .0001" of each other.
Not a method that will work for everyone, but the concept can be applied in other ways. My arms are 340mm between centers.

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GroupB
its nothing virtual.. its how you measure the arm length... its always been a measure pivot to pivot whatever you use magnetic,rc car joint or any others form of joint

I use the word virtual to mean that the arm length measurement in my case is actually not the length of the physical rods as the pivot point is 5mm past each end of the cup bottom on each end of the physical rod.

Apologies for mixing terminology.

One jig coming up to get the measurement with balls in the sockets on each end to correctly determine the pivot to pivot distance which i then assume is the number used in the firmware for delta rod length?

Measuring the exact length of the arms isn't really necessary. Having them the same length plus or minus a handful of microns is important. The formulas used during calibration (to get a level print bed) will tell you within a few microns what the length of your arms are.

Only if your bed si so big that your print head can get significantly behind the line connecting two virtual tower positions. Most delta printer do not have this property. Therfore for most printers, the calibration procedure will drift and will not find the proper arm length and delta radius. Of course you could optimize only arm length and not delta radius (tower positions) but that would mean that you can precisely measure delta radius which is much harder than measuring arm length.
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hercek
Only if your bed si so big that your print head can get significantly behind the line connecting two virtual tower positions. Most delta printer do not have this property. Therfore for most printers, the calibration procedure will drift and will not find the proper arm length and delta radius. Of course you could optimize only arm length and not delta radius (tower positions) but that would mean that you can precisely measure delta radius which is much harder than measuring arm length.
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I don't follow "can get significantly behind the line connecting two virtual tower positions". my bed has grown as the build has progressed to the point that the 500mm rods are far to short to cover the full bed so definitely fall into a BIG bed area now.

Draw a line connecting center of your bed with center of each tower.
Virtual tower is on that line. It is (carriageOffset + effectorOffset) far away from the center of the real tower.
Connect the virtual tower positions to form a triangle.

The more you can probe outside that triangle (and the more the arms are horizontal when probing there) the higher the chance that the calibration math can correctly find both tower positions and the diagonal rod length.

E.g. it is good if you can probe about 50% behind that triangle line (i.e. 100% is from bed center to the line and the additional 50% is from the line to the actually probe point). This is just an example I did not try to derive exactly the necessary condition when the calibration will properly separate delta radius from diagonal rod length. The necessary condition would depend on the probing error, printer geometry, and the bed geometry.

The conclusion for people who do not want to play with math is: do not assume that the calibration procedure will fix both delta radius (tower positions) and diagonal rod length.

Thanks hercek,

I had to read it a couple times then it did sink in, a quick mock up in tinkercad shows that once I get new arms to allow full bed coverage I should get 50% past the line with no issue.

the tower to tower distance is close to 640mm now since I made the hexagonal sides 345mm long

Cheers

Thanks for the responses regarding measuring the arm lengths. I looked through my box of kit and came up with the following method which may give others some ideas:
Equipment was:

• Internal Micrometer (bore type)
• Gauge blocks (Johanssen blocks)
• 2 pieces of 3mm Silver Steel (Drill Rod)

I used the silver steel to construct the original arms (glue one end of the rod to a Traxxas joint, allow to dry, thread the eyes of the 6 rods with one piece of silver steel, then glue up the other 6 and thread them through as well. Ensure that the two pieces of silver steel are parallel and voilà!) so thread the joints onto the two pieces of silver steel to form a parallelogram and square up as much as possible.
I then wrung together the 4", 3", 2"and 0.8" blocks and placed them as shown in the photo and added the 1" block at the other end to provide a firm and square face for the micrometer.
place the micrometer in the gap between the blocks and measure (2.241").
The centre distance is then the sum of the 5 blocks (10.8") plus the micrometer's 2.241 plus 2 x the half thickness of the silver steel rods (3mm = 0.1181") = 13.159" or 334.241mm...

I was fortunate to have the gauge blocks but any parallel blocks that can be measured separately could be used (although every block adds a separate error, probably too small to worry about).
IMG_1863 by simon0362, on Flickr

IMG_1864 by simon0362, on Flickr

IMG_1865 by simon0362, on Flickr

Edited 1 time(s). Last edit at 04/28/2016 06:08AM by Simon0362.

what do arm sizes just the rod depend on i know its a newbie question but ive seen mini kossels with variant lengths from 180mm. i am trying to figure out the size i seen in wiki 180mm but i bought 300m carbon rod just to make sure i had enough material and want measure twenty times and cut once so any help be totally grateful thanks

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