# Turner's Cube (Manual Machine)

10 Steps
Once upon a time, one of my teachers at school brought in a Turner's Cube.  He showed it to us, as well as the cube with a sphere in it.  He was showing things that you could make on the CNC machine, and I thought the cube was amazing.  I knew I wouldn't be able to make a sphere on a manual machine, but a cube within a cube within a cube?  That didn't seem too bad!

And so the quest began!  I began researching Turner's Cubes, and I found information about CNC projects, turners cube calculators, and all that jazz (I even found some that this guy was making on a wood lathe, with all sorts of amazing shapes inside.  Dodecahedron's and the like).  But nothing on a manual machine!  Something had to be done.  I figured out how to make one, made a few prototypes, and once I got a nice one done I came here to share it with you!  Here is an Instructable on how to make a Turner's Cube, on a manual lathe (and mill).  I'll go through the calculations and everything, so you can make one of any size with any number of cubes!

I think this is an appropriate entry for the "Make it Real" challenge, because this is a project that is hardly ever done on a manual machine, it is usually made on a CNC machine.  I believe that making something with your hands and on manual machines  "makes it real" more then programming a robot to make it for you does.  I made models in Google Sketchup and Autodesk Inventor, and have attached the files here.

This project is actually not as hard as it looks, so don't get discouraged by how complex it looks.  Here are the skills you need to be able to make this:
- Working within a +/- 0.005 tolerance (any more and it looks off)
- Dialling in a milling machine (to as tight a tolerance as you can get it, 0.001-0.002 is the goal)
- Using a face mill + planar bar on a mill to make the cube
- Facing cuts on a lathe
- Boring flat bottomed holes on a lathe
- Undercutting on a lathe
- Know how to dial in work pieces on a 4 jaw chuck

All in all, this is maybe an 8 hour project.  Once you get all the tools ready, and know what you're doing, it's less then an hour a side. (times 6 sides, and the the time to mill a cube)

Tools/material needed:

- Aluminium stock
- Milling Machine
- 3 in face mill
- Planar bar
- Bandsaw
- Lathe with a 4 jaw chuck (or some sort of fixture to hold the cube, 4 jaw is easiest)
- Grinder (for making the HSS tools)
- Dial indicator with a magnetic back
- Dial indicator with a magnetic base
- Live centre (to set your tool heights to centre)
- Drill chuck (to hold the drill bits)
- Tool holder (for your HSS bits)
- Boring tool for the lathe (I'll show you how to make one out of High Speed Steel (HSS))
- Undercutting tool (again, I'll show you how to make one out of HSS)
- 90 degree chamfering tool (made out of HSS)
- Countersink to reach the smallest hole (5/8, if you use my numbers, if you make your own numbers, you may need smaller)
- Drill bits (to help rough out the bores)
- Files for deburring at the end
- Measuring tools (calipers or micrometers and telescopic gauges.  I like calipers)

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## Step 1: Calculations

To start out your Turner's Cube, you need to figure out how big you want it to be, and how many cubes you want.  3 cubes is a good number to start with.  But you could make any number.  These calculations are a guideline, and an example of how I made it.  Substitute your own numbers to make your cube unique.

To start, we had 2in x 2in aluminium stock.  So the cube was going to be less then 2 inches.  1 7/8 (1.875) seemed like a good size to make.  I wanted 3 cubes, so I took 1.875 and divided it by 3, so I would know how big each cube will be. 1.875/3= 0.625, so the size difference between each cube will be 0.625 (5/8).  The cubes will be 0.625 (5/8), 1.250 (1 1/4), and 1.875 (1 7/8).  Now I needed to figure out how big the bores are going to be.

When calculating the bores, you need 2 numbers.  One will be the diameter of the bore, and one will be the diameter of the undercut. The diameter of the bore has to be smaller then the corner to corner distance of the cube that will be contained within, and the undercut has to be bigger.

So, for example, my smallest cube is 0.625.  The corner to corner distance on this cube is 0.884 (Pythagorean Theory, A^2 + B^2 = C^2).  So, the opening of the bore has to be less then that, and the undercut has to be greater then that.  I made the bore opening 0.750.  You can open any simple modelling software (Google Sketch-up is nice, and its free!), and draw your cube, and then draw some circles on it to see what size looks good.  The undercut I made 0.200 bigger, so the diameter was 0.950.  The bigger cube is 1.250, so there is still plenty of material left.

Let's repeat the calculation for the next size.  The cube is 1.250, so the corner to corner distance is 1.768. (sqrt(2*(1.250*1.250))).  The bore opening is 1.500, and the undercut is 0.350 bigger, so 1.850.   As for the smallest hole, you can usually just use a drill bit.  Again, draw some circles and see what size would work, then pick a nice drill bit.  I used 9/32.

Now we need to calculate the depths of the bores.  To do so, we need to calculate the red distance, and the green distance.  (Picture #1) For the red distance, take the biggest cube (1.875) and subtract the smallest cube (0.625) to get 1.250, and divide that by two, since we're only working on one half of the cube at a time.  So the depth of the first bore is 0.625 ((1.875-0.625)/2 = 0.625).  For the second, take the biggest cube (1.875), subtract the middle one (1.250) and divide by two again to get 0.3125, rounded to 0.313.

Now we have all our dimensions!  The cubes will be 1.875, 1.250, and 1.625.  The hole in the middle is 9/32. The bores are 0.750, 0.625 deep, with a 0.950 undercut, and 1.500, 0.313 deep, with a 1.800 undercut.

Onwards to construction!
Chris Logan says: Jan 6, 2013. 12:29 PM
You can make a sphere in a cube... Using an inverse ball endmill plunged from all six sides.
Xyver (author) in reply to Chris LoganJan 6, 2013. 2:30 PM
I was wondering how to do that... We saw an example of that, but it was made on a CNC. I imagined it was just a small endmill (<1/4 in) and some fancy programming to get the angles required for the circle. But inverse ball endmill would be perfect!

It would still be a bit tricky though, because you'd have to make the hole smaller the the diameter of the ball, and that would make it tricky to get the endmill in.

I may be getting some more time in a machine shop.... Perhaps I should try it to see how it works out.
Chris Logan in reply to XyverJan 6, 2013. 11:33 PM
The endmill dictates the hole diameter.

When I was in machining school (Warren Occupational/Technical Center in Lakewood, CO), we learned to grind the radius into the endmill. The trick, for this part, is to cut a larger radius than the cutter. The resulting ball will be larger than the hole when plunged through from six sides. But will remain attached to small support surfaces at the corners.... This is serendipitous, as you wouldn't want the aluminum ball coming free and bouncing into your fragile cutter anyway.

Once the manual machining is complete, Go back in with a jeweler's saw and free the ball.
Xyver (author) in reply to Chris LoganJan 7, 2013. 12:16 AM
Ahhh.... But then you'd have rough saw marks on the ball...

If you did plunge in fully on 5 of the sides, on side 6 you could stop, and do similar to what I did in Step 7, for the final side. Just stop the mill, and turn it by hand, so the ball falls off nicely and you dont have to deal with it spinning at upwards of 1000 RPMs :D
Chris Logan in reply to XyverJan 7, 2013. 7:43 PM
If you plunged it completely on 5 sides, you'd have a sphere that isn't very spherical.

You clean the jewelry saw marks up by hand with your trusty needle files and maybe sandpaper. A machinist worth his salt can turn file marks into replica machine-tool marks. I do it often... And polishing the whole assembly to a bright finish is even easier.
ddw_az says: Mar 18, 2012. 8:04 AM
VERRY GOOD!
i use to do this by hand in Wood.
Xyver (author) in reply to ddw_azMar 21, 2012. 11:23 AM
Do you have and pictures of wooden ones you could share?
ddw_az in reply to XyverMar 21, 2012. 5:23 PM
these are my Uncles. My mother has mine
i have done copies of all of these Except the 3-interlocking rings on the left

Xyver (author) in reply to ddw_azMar 23, 2012. 1:43 PM
Pretty wicked! Should try making some of these out of metal
ironsmiter in reply to XyverMay 1, 2012. 7:34 AM
it MAY be possible. I'd love to see it if it is.

however, the wooden models are only possible because of the ability to use a knife and the sheering properties of woodgrain.

One whittles down most of the joint, SNAPS the remaining web, then uses the knife and sandpaper to smooth out the roughness.

To achieve the same results in a machine operation, using metal, would probably require an EXTREMELY delicate bit, a very high rpm machine spindle, and a 5-6 axis machine. The very fine, fiddly work your hands do naturally with a knife blade are impossible to replicate in a 4 axis machine. And nearly impossible in a 6-axis.

Check out the 5:30 mark on this youtube video for the sort of fiddly maneuvers needed by a machine tool to replicate a fairly simple hand-tool woodworking process. http://www.youtube.com/watch?v=GU32Q6QXtWQ

You COULD replicate these in metal, fairly easily, but it would involve casting, not machining.
ddw_az in reply to XyverMar 23, 2012. 4:57 PM
here are some better photos of the plier joints
Apr 24, 2012. 2:27 AM
Looking at this actually makes me giddy. I love it.
FirstAttempt says: Mar 14, 2012. 2:57 PM
This is really cool, I took a manual lathe class as a pre-req for a bunch of engineering classes a few months ago, I think I'll try this.
Xyver (author) in reply to FirstAttemptMar 21, 2012. 11:23 AM
Do it!
codongolev says: Mar 19, 2012. 6:05 AM
now I know what I'm making when I gain access to the lathe at my college (and learn to use it). I remember the first time I saw one of these, I just thought and thought and thought until I figured out how it was made. it's shockingly simple, you just need good spatial sense.
Xyver (author) in reply to codongolevMar 21, 2012. 11:23 AM
Most things are a lot simpler then we think they are. Just take it one step at a time, and before you know it, you're done!
blanchae says: Mar 18, 2012. 9:19 AM
Little typo: "Male it Real" challenge. Thought that I was reading Cosmopolitan for a minute...
Xyver (author) in reply to blanchaeMar 18, 2012. 12:25 PM
Oh my! Thank's for pointing that out. Fixed!
ironsmiter says: Mar 15, 2012. 4:42 AM
WONDERFUL!

You beat me to it, but glad to finally see a REAL turners cube!
Not saying the "attached nested cubes" aren't fun to look at, but this requires a great deal more skill. And make better playthings for when you have grandkids.
Also glad to see you did the double nested version(so much more impressive than a one-in-one)

As I understand it, this was an apprentice job way back in the day.
And it was done entirely on a lathe(this being WELL before computers, heck most shops at the time didn't even have electricity!)
It was a testament to the young man's skill, to be able to make the 6 facing cuts, to get a cube. Ok, it was a REQUIRED BASIC SKILL. :-)

Step 11, on the final side cutting... that's an interesting technique!
Sure would have been quicker than how I did it.
I ended up making 5 stepped plugs, with 1-2 thou clearance.(4 jaw chuck, plus a backing plug). Obviously, all 5 plugs were turned on the same lathe.
The main advantage to having plugs is, you can have the machine running the whole time. You don't have to turn the chuck by hand for the last bit. Also eliminated the need for using your shims :-)
Xyver (author) in reply to ironsmiterMar 18, 2012. 12:25 PM
I'm just finishing up my final project at school, then I'm going to make the "attached nested cubes" (4 cubes) and a free floating one like this, but with 5 cubes instead of 3 :D I'll be sure to add them to this Instructable!
sitearm says: Mar 18, 2012. 10:50 AM
@Xyver; tweeted! Love the arcane vocabulary (is not a miller) Cheers! : ) Site
Dream Dragon says: Mar 12, 2012. 5:20 AM
Thanks for sharing a very detailed and well presented instructable. though it's rarely done now, it certainly USED to be a very common way for a turner to show his skills. When you talk about using a "manual" machine you are of course only adjusting the machine manually,consider doing the same kind of thing with a "Pole Lathe" or "Treadle Lathe", it HAS been done, but not my me.
Xyver (author) in reply to Dream DragonMar 12, 2012. 10:26 AM
I'm mainly talking about manual vs CNC, where we control the machine as opposed to robots controlling the machine.

I can only imagine how tiring a treadle lathe could be.....
ironsmiter in reply to XyverMar 15, 2012. 4:26 AM
you might be surprised how NOT tiring it can be ;-)
Cunning_Stunt says: Mar 14, 2012. 12:33 PM
I made one of these when I was training. They are quite impressive and I'm still pretty proud of it :)
Thanks for sharing, I hope it inspires people to make one.
rimar2000 says: Mar 12, 2012. 3:56 AM
Nice and detailed instructable, thanks for sharing.
Xyver (author) in reply to rimar2000Mar 12, 2012. 10:26 AM