Turning pentagons on a lathe

[tonyfoale]

Jon recently posted a video ( Polygonal turning tool - video ) showing the method of turning polygons, multi-sided shapes, on a lathe using a rotating cutter. This was new to me but a quick internet search showed that it was a well known technique applicable for home hobbyists with limited facilities, as the video shows, as well as commercial users and is even used on CNC lathes. Even with CNC it is faster than some other methods such as indexed milling. metric-taper added to Jon's post with another homemade effort, albeit more complex. Here is a sample image of that



To satisfy my curiosity I needed to understand the mathematics behind this bit of magic. Internet searches came up with absolutely nothing. So I had to derive the expressions myself. I was expecting some complex geometry to solve but the reality is that the mathematics are very simple. I then prepared a design and understanding tool in the form of a spreadsheet to draw the shapes that could be made and that can be downloaded from https://diqn32j8nouaz.cloudfront.net...on_turning.xls.
I have also prepared a PDF file which gives a full explanation of how this method works and that can be downloaded from
https://diqn32j8nouaz.cloudfront.net...on_turning.pdf

Here are some sample images from the spreadsheet:

Click for full size images.
On the left is a hexagon formed with a gear ratio of 2 and 3 cutters on the cutting shaft. Workpiece and cutters rotating in the same direction.
On the right we see a gear ratio of 3, 1 cutter and opposite sense rotation.



Both of these 4 sided shapes are cut with a 2:1 gear ratio with 2 cutters, the only difference is the sense of the rotation, same sense on the left and opposite sense on the right.

The spreadsheet is a useful design tool for anyone using this turning technique, read the PDF and it will become crystal clear. For those who want the full story the derivation of the simple mathematics is included.

Of course we need the obligatory video, just 50 seconds of Youtube shorts, this shows a slow animated simulation which clearly demonstrates the interactions between the cutting edges and the workpiece, resulting in a near straight surface. The parameters of the simulation were a gear ratio of 2:1, the cutter radius was double the workpiece radius, rotation was same sense and one cutting edge. In reality this would cut a two sided figure but the simulation is limited to one.

[DIYer]

Thanks tonyfoale! We've added your Pentagon Cutting Method to our Machining category,
as well as to your builder page: tonyfoale's Homemade Tools. Your receipt:

Pentagon Cutting Method by tonyfoale

tags: machining

[BuffaloJohn]

A pentagon is a five sided polygon, what you have shown is a hexagon. What am I missing?

[tonyfoale]

A pentagon is a five sided polygon, what you have shown is a hexagon. What am I missing?

Brain fart, all fixed now.

[Toolmaker51]

I'll have to examine my Lyman tumblers (they work well on cartridge cases) to see if import versions utilize original logical mechanics and physics.

Tony, by his nature, wired any classes in practical physics long ago. Such physics are as much visualization as is theory, hypotheses and computation.
There is a sizable population without capability to work those together; yes it's true!

Started watching here in hmt.net; got distracted and it finished. Of course the usual suggestions popped up, so finished in youtube.com.

If there is any proof in the decline of mechanical ability, indolent students, and those unable to follow a clear discussion; it's loud and clear in the comments section.
Wow.
One clearly a type, expecting the professor to show up and do it for him.
Wow again.

[gatz]

That’s very interesting. Gonna have read it a few more times to fully understand it.
Mentioned in the animated video is “near flat surfaces” what does that mean?.. flat within what?
the Russian(?) version seems to be well thought out. In lieu of a chain drive at the end of the lathe bed, perhaps a heavy-duty drive belt or an Eagle drive belt
would satisfy the needed flexibility requirement and would be less noisy.
The CV joint looks like it would work nicely.

[Toolmaker51]

Mentioned in the animated video is “near flat surfaces” what does that mean?.. flat within what?

Flat as performed by a rotating cutter on the same axis, the amount dependent of width of face in question.

Not forever, but this capability is in multi-axis CNC lathes, though most run a mill on each face been around a while.
At any rate, those cutters are driven, timed with but not connected to main spindle and called "live tools". Slitting, drilling, milling, engraving, of features in place, versus secondary work on other machines.

[tonyfoale]

That’s very interesting. Gonna have read it a few more times to fully understand it.
Mentioned in the animated video is “near flat surfaces” what does that mean?.. flat within what?

The examples in the PDF show how the flatness of the sides is dependent on the basic parameters. The eXcel file allows you to play with parameters and see just how near flat any particular combination of parameters will produce.

[tonyfoale]

Flat as performed by a rotating cutter on the same axis, the amount dependent of width of face in question.

The rotating cutter has to be on a different axis or it can only cut circular shapes.

Not forever, but this capability is in multi-axis CNC lathes, though most run a mill on each face been around a while.
At any rate, those cutters are driven, timed with but not connected to main spindle .

When this technique is applied to manual machines the cutter spindle is connected to the main spindle through mechanical means to achieve the timing and appropriate gear ratio.

[tonyfoale]

I'll have to examine my Lyman tumblers (they work well on cartridge cases) to see if import versions utilize original logical mechanics and physics.

You may find this earlier post on vibratory tumblers to be of interest, I suggest watching the video all the way through.
Fixing more Harbor Freight stuff. Vibrating Tumbler.