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 in 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)
- Aluminium stock
- Milling Machine
- 3 in face mill
- Planar bar
- 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)
Step 1: Calculations
WARNING, TRIGONOMETRY AHEAD!!!
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!