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How to fit a Round Peg into a Square hole
August 31, 2009 1:13 PM   Subscribe

Drilling a Square Hole. Can a drill be constructed which makes square holes?
Previous attempts have focused on Reuleaux triangles (a shape of constant width - useful for manhole covers) - but these produce square holes with rounded edges.
However, in 1939, in an anonymous article in Mechanical World magazine, plans were published for a device which uses circular motion to make perfectly square holes.
In their new book, How Round is your Circle, John Bryant and Chris Sangwin, build and demonstrate this device (scroll down for a video of the working device).
posted by vacapinta (78 comments total) 37 users marked this as a favorite

 
Nifty. Now it's just too bad there's no way to mount such a thing on a regular old power drill.... since if I am following along correctly, there's no fixed point to press the drill into.

So some sort of clamp would have to hold it in place, is that right?
posted by rokusan at 1:19 PM on August 31, 2009


Looks like the device leaves very rounded corners. Still pretty cool.
posted by billysumday at 1:25 PM on August 31, 2009


My post on linkages contains comments with more animations of these sorts of devices, which translate rotation into motions with linear and rectilinear effect.
posted by Blazecock Pileon at 1:27 PM on August 31, 2009 [2 favorites]


Here's a Wolfram demonstration showing how the device works.

billysumday: No, previous devices left rounded corners. This one leaves angular corners.
posted by vacapinta at 1:28 PM on August 31, 2009 [1 favorite]


O REULEAUXY?
posted by It's Raining Florence Henderson at 1:28 PM on August 31, 2009 [28 favorites]


I would be curious to see this drill actually being used to drill a hole, as opposed to being in a hole already. Unless I missed a link somewhere?

None the less, very cool.
posted by Joey Michaels at 1:32 PM on August 31, 2009


Here is a bike based on the same principle. Interestingly, you can turn this around to make a bike with square wheels that rolls on a catenary surface.
posted by phrontist at 1:32 PM on August 31, 2009


> No, previous devices left rounded corners. This one leaves angular corners.

The tip of the drill describes a perfectly square path, but the tip is the center point of the circular profile of the drill; once it cuts into material the square will still have rounded corners.
posted by ardgedee at 1:33 PM on August 31, 2009 [2 favorites]


video
posted by phrontist at 1:34 PM on August 31, 2009


This is going to sound stupid but...is this just a thought exercise or is there some sort of need for square holes that I don't know about?
posted by JoanArkham at 1:34 PM on August 31, 2009


Joan, square pegs.
posted by klangklangston at 1:37 PM on August 31, 2009 [2 favorites]


I've always been fascinated with Reuleaux triangles, especially in that last application mentioned -- rotary engines. That Mazda successfully mass-produced them is even more impressive.
posted by spiderskull at 1:37 PM on August 31, 2009 [1 favorite]


...aaaaand It's Raining Florance Henderson wins the thread!!! Tell him, Bob, what he's won!!!

Okay in all seriousness, this is an amazingly neat tool. Angular square holes with a drill... I'd sure like to have one in a workshop. I could imagine that a tool like this would net be cheap.
posted by PROD_TPSL at 1:38 PM on August 31, 2009


vacapinta: I'm just going by the video you posted. Clearly, the demonstration shows huge gaping holes in the corners. If there's a video I missed that shows the bits getting to the corners, I'd love to see it.
posted by billysumday at 1:38 PM on August 31, 2009


Well, you need something to not put round pegs in.
posted by nebulawindphone at 1:40 PM on August 31, 2009 [1 favorite]


Ah, I see. I thought the wedge was the blade. It's just the form that the blade is in. Got it.
posted by billysumday at 1:40 PM on August 31, 2009


Couldn't a laser beam be focused to a square shape, and that used to drill the hole?
posted by zabuni at 1:40 PM on August 31, 2009


Couldn't a laser beam be focused to a square shape, and that used to drill the hole?

Laser beams are good for cutting spies in half and cracking safes, but probably not so good for cutting holes in flammable wood.
posted by Blazecock Pileon at 1:48 PM on August 31, 2009 [1 favorite]


Why not just use a mortising bit?
posted by JeffK at 1:49 PM on August 31, 2009 [8 favorites]


Couldn't a laser beam be focused to a square shape, and that used to drill the hole?

That's impossible; even for a computer.
posted by The World Famous at 1:53 PM on August 31, 2009 [5 favorites]


This is going to sound stupid but...is this just a thought exercise or is there some sort of need for square holes that I don't know about?
posted by JoanArkham at 9:34 PM


This is more of a geometry and math post, which means none of this is necessarily practical.
posted by vacapinta at 1:54 PM on August 31, 2009


...aaaaand It's Raining Florance Henderson wins the thread!!! Tell him, Bob, what he's won!!!

Don't encourage him when he's being a cam whore.
posted by cortex at 1:58 PM on August 31, 2009 [11 favorites]


This is more of a geometry and math post...

I was told there would be no math.
posted by The Deej at 1:58 PM on August 31, 2009


This circle squaring tool runs on a perpetual motion engine, I take it.
posted by Joe Beese at 1:59 PM on August 31, 2009 [1 favorite]


I wonder if you got the right ratio of the length of the crank arm to the motion of the cutting head if this thing would literally square a circle and preserve the area properly. I guess since you could size the crank arbitrarily it would be pretty simple.

EAT THAT ANCIENT GREEKS!
posted by GuyZero at 2:04 PM on August 31, 2009


It is not math until it is generalized to an n-dimensional tool to generate n-1 dimensional hypercubes.
And then a physicist generalizes it to some ballsy assumption about the universe.
And then SciAm publishes an article simplifying it to "Scientists agree: Earth is square!"
posted by qvantamon at 2:04 PM on August 31, 2009 [5 favorites]


Archaeologists everywhere are pricking up their ears, and laying down their trowels.
posted by Rumple at 2:08 PM on August 31, 2009


GuyZero, I think to meet Greek standards it would have to have rational ratios between wheels (also, for practical purposes, so you could fit cogs in there). Or at least the whole setup (including ratio transformation) would have to be buildable with rational lengths and compass and ruler setups.
posted by qvantamon at 2:09 PM on August 31, 2009


The most elementary logic would tell you that you can't, ever, drill a perfectly square hole with a round drill. You may be able to get the rounded corner so small as to not matter for your application but it's never going to be a perfectly square hole.
posted by Justinian at 2:09 PM on August 31, 2009


Joan, you need square holes (and rectangular ones, which you can make with a series of squares) in order to do traditional wood joinery like mortises. Using a drill beats chiseling them by hand. But the furniture industry has that problem solved for wood, as JeffK shows.
posted by echo target at 2:10 PM on August 31, 2009


Justinian, it's not using a rounded drill bit, there's a wedge-shaped blade that traces a square path.
posted by echo target at 2:11 PM on August 31, 2009


The tip of the drill describes a perfectly square path, but the tip is the center point of the circular profile of the drill; once it cuts into material the square will still have rounded corners.

Well, it's easy, just make the drill bit in a reuleaux triangle shape and have it move in the appropiate path and viola! you have square holes.

It's turtles all the way down....
posted by Confess, Fletch at 2:23 PM on August 31, 2009 [2 favorites]


> The tip of the drill describes a perfectly square path, but the tip is the center point of the circular profile of the drill

Actually, now that I think about it, the tip could represent the outermost point of the leading edge of a cutting blade, making this not as stupid as I had previously thought as long as the mechanism can guide the blade appropriately to cover the whole square surface without twisting under force. Apologies to vacapinta.

And to answer another question, the ability to mass-produce square holes rapidly is useful in a variety of contexts, although I have no idea whether this device can contribute to the progress of mechanical engineering.
posted by ardgedee at 2:31 PM on August 31, 2009 [1 favorite]


Unless you're removing material atom by atom from a cubic or orthorhombic crystal, no perfectly square holes exist in nature, just holes where the corners have an arbitrarily small radius of curvature. Good enough for me!
posted by adipocere at 2:34 PM on August 31, 2009 [2 favorites]


Laser beams are good for cutting spies in half and cracking safes, but probably not so good for cutting holes in flammable wood.

Nah, you can cut all sorts of stuff with lasers. I know they're used for cutting fabric for clothing.
posted by ryanrs at 2:40 PM on August 31, 2009 [2 favorites]


Um, the Reuleaux triangle article in the FPP says that Wankel rotary engines are not in that class.
posted by mkb at 2:41 PM on August 31, 2009


I can imagine the discussion going on...
"We need to cut a perfect square... we can use math..."
"BORING!"
"...or we can use lasers!"
"LASERS!"
posted by qvantamon at 2:42 PM on August 31, 2009 [4 favorites]


Laser beams are good for cutting spies in half and cracking safes, but probably not so good for cutting holes in flammable wood. - The Multifarious Mr. Blazecock Pileon

That, my dear Mr. Pileon, is why you use inflammable wood.
posted by Mister_A at 2:42 PM on August 31, 2009 [6 favorites]


GuyZero, I think to meet Greek standards it would have to use a compass and straightedge, which is somewhat beyond the means of contemporary drills.
posted by kenko at 2:44 PM on August 31, 2009


Actually, now that I think about it, the tip could represent the outermost point of the leading edge of a cutting blade, making this not as stupid as I had previously thought as long as the mechanism can guide the blade appropriately to cover the whole square surface without twisting under force. Apologies to vacapinta.

I meant to put the Wolfram widget link in the main post. It makes it clearer how your cutting blade idea would work (click on 'watch web preview' in the upper right)
posted by vacapinta at 2:59 PM on August 31, 2009


Doesn't a Reuleaux triangle's corner have an interior angle of 120°? How can it ever touch the corner of the containing square?
posted by equalpants at 2:59 PM on August 31, 2009


Ah, my bad, I got the squares mixed up. Hey, this is pretty cool.
posted by equalpants at 3:01 PM on August 31, 2009


Square holes are made all the time, but not with that wacky drill. One of the oldest ways is to drill a round hole a little smaller than the width of the square desired and then press a broach through the hole. The broach has many cutting blades which transition from the previous circle drilled on one end to the square desired on the other. Unfortunately, a separate broach is needed for each size square hole required. For that reason, square holes are usually specified as a common size. If an oddball size is required, a broach could be reground as required but they're not cheap to begin with.
posted by digsrus at 3:20 PM on August 31, 2009 [2 favorites]


Laser beams are good for cutting spies in half and cracking safes, but probably not so good for cutting holes in flammable wood.

Actually, they're excellent for wood and other inflammable materials. Ponoko for example offers lots of kinds of ply, customwood and what have you as materials for laser-cutting.

Don't laser-cut leather though, because the smoke stinks like nothing you ever smelled before. And don't laser-cut shiny metal, because the beam reflects back and fucks up your lens.

Finally, remember that great advice: DO NOT LOOK INTO LASER WITH REMAINING EYE.
posted by i_am_joe's_spleen at 3:20 PM on August 31, 2009 [6 favorites]


OK, I clicked on all the links (except the first one in the FPP - it seems to be shy), and I have a few things to say. None of those demonstrations , simulations, animations, or flagellations show a hole being made. Every hole-cutter I own has a sharp edge somewhere. None of the things in the link have any sharp edge that I can see. The so-called "demonstration of the working device" shows what looks like a cam follower. It isn't cutting anything. If you're going to tell me you're demonstrating drilling a hole, I want to see some chips. Otherwise, I don't believe this thing will cut.

Besides JeffK's mortising bit for making square holes in wood, there are tools for making square holes in metal, called broaches. You have to make a round hole first, as with mortising, then the broach is pushed through, and its teeth incrementally carve away the corners until the hole is square. A CNC laser or plasma cutter could also make a square hole.
posted by Kirth Gerson at 3:21 PM on August 31, 2009


I am joe's spleen sort of beat me to it, but more specifically:

Alex Henderson laser cuts jewelry from walnut.
posted by Extopalopaketle at 3:27 PM on August 31, 2009


Um, the Reuleaux triangle article in the FPP says that Wankel rotary engines are not in that class.

Huh, I stand corrected.
posted by spiderskull at 3:31 PM on August 31, 2009


And if you're not already bored to tears, a wire EDM (electrical discharge machining) machine can be used to make a square hole. In this case a hole is drilled through the workpiece through which a wire runs off of one spool and is threaded through the hole and then onto another spool. Then an electrical current large enough to chip off a little material but not big enough to melt the wire is passed through the wire into the workpiece. A conductive oil washes out the chips as the wire is very slowly moved both into the workpiece and from spool to spool under computer control. It takes a very long time to complete the hole but sometimes the hardness of the material the workpiece is made of makes this the only method which works.
posted by digsrus at 3:37 PM on August 31, 2009


Kirth Gerson: the "working device" is just the mechanism that the sharp edge would be mounted to. You can see the sharp edge in the Wolfram link (arrow pointing to it in this image). Are you just saying that nobody would actually make a product based on this mechanism? Of course nobody would. It's mainly a cool thought/mechanical experiment. Given the size of the mechanism, you wouldn't be able to make a very deep square hole with it; you'd be limited by the depth of the chisel that'd be mounted to it.
posted by zsazsa at 3:38 PM on August 31, 2009


> I meant to put the Wolfram widget link in the main post. It makes it clearer how your cutting blade idea would work (click on 'watch web preview' in the upper right)

That confuses things more rather than less, because it assumes the blade is exactly 90 degrees to the plane of the surface being cut and is of vanishing thickness at the outermost edge. You'll go through a lot of blades that way.
posted by ardgedee at 3:39 PM on August 31, 2009


oh no they di'int!
posted by sexyrobot at 3:48 PM on August 31, 2009


Are you just saying that nobody would actually make a product based on this mechanism?

No, I'm saying that the things I expected to see from what was written in the post:
Can a drill be constructed which makes square holes? ... John Bryant and Chris Sangwin, build and demonstrate this device...
don't actually happen. The demonstrated device will draw a square if you put a pencil in it. It remains to be seen if it will cut a square hole.
posted by Kirth Gerson at 3:51 PM on August 31, 2009


Heh. This thread for me points out why there is often a deep divide between theoreticians and experimentalists in any field. I'm a pure math geek. It was interesting to me only that the mechanism exists, at least ideally, mathematically. I thought other geeks might be interested in this variation on a Reuleaux triangle as a pure mechanism. The first link is to a Mathematics magazine. It also appears that the mechanism can be generalized to make regular N-gon holes where N is even - such as a hexagon.

Honestly, whether this mathematical thing can actually be built into something to drill square holes or whether there are other ways to make square holes never entered my mind for a second.
posted by vacapinta at 3:51 PM on August 31, 2009 [3 favorites]


If Timecube finds out about this I wonder if he will make a Drillcube subpage.
posted by Antidisestablishmentarianist at 4:02 PM on August 31, 2009 [2 favorites]


Heh. This thread for me points out why there is often a deep divide between theoreticians and experimentalists in any field.

Yeah, and I guess I'm in the same camp as Kirth Gerson: I want to see something being cut, machined, or milled, or, in lieu of those noble actions, blown up or shredded. Also acceptable: being dropped from a height, set ablaze, or launched from a trebuchet.

However, despite the blatantly false advertising, I greatly enjoyed this post and the accompanying links.

In return, please enjoy this dangerously non-theoretical turbocharged barstool.
posted by mosk at 4:10 PM on August 31, 2009 [1 favorite]


All that said, here's some pictures of Watts drills which are the "predecessors" of this design. They are being manufactured and used.
posted by vacapinta at 4:10 PM on August 31, 2009


Roy Underhill shows how to drill a square hole in wood using vintage tools starting at 4:40 in this video.
posted by _caliper_ at 4:50 PM on August 31, 2009 [1 favorite]


I want one of these drills and I can't for the life of me figure out why.
posted by gordie at 5:34 PM on August 31, 2009


I always thought this would be useful for tunnel boring machines for
roadways (such as still-controversial planned Seattle deep-bore tunnel to replace the Alaskan Way Viaduct).

A circular tunnel put limits on the number of lanes due to height restrictions on the sides. A square tunnel (or a rectangular one with squares bored out side-by-side) would have less wasted space.

But then the square tunnel without an arch, would probably lack the strength of a round one.
posted by ShooBoo at 5:36 PM on August 31, 2009


Inspired by Exploratorium's reuleaux triangle device, I once built a rolling tetrahedron for a children's physics kit. Rolling cube, too. Take a normal tetrahedron and bow the edges outwards to form sections of an ellipse. Carve some examples out of ppma. Put two on an axle and they roll smoothly. Viewed from the end, they're cylindrical.

SQUARE WHEELS
posted by billb at 5:51 PM on August 31, 2009


"This is going to sound stupid but...is this just a thought exercise or is there some sort of need for square holes that I don't know about?"

All sorts of need for square holes. EG: carriage bolts in metal plates.

"Laser beams are good for cutting spies in half and cracking safes, but probably not so good for cutting holes in flammable wood."

Actually very useful. I'd like to add a laser to my cnc router at some point in the future capable of cutting up to 3/4" plywood. Besides the great reduction in waste because of the elimination of a physical cutting head a laser doesn't apply any side force to the material meaning clamping needs are greatly reduced to the point of almost being eliminated. Plus MDF is really abrasive so eliminating a cutting edge with that material would be a significant cost saving depending on the maintenance costs of the laser.
posted by Mitheral at 6:16 PM on August 31, 2009 [1 favorite]


For structural square holes, rounded corners are preferred in most cases, as perfectly sharp corners will promote cracking. The rounded-corner work is is generally done with a milling machine in precision machining, though lasers and EDM are making inroads in terms of cost.

As others have mentioned, the devices shown are not cutting tools, and have neither cutting edges nor any sort of flutes to carry away the waste material once it has been cut. It does present the theory for how to build a single-tool, square-hole cutter though, so that's kind of interesting. The only use for that I can picture though would be in a mass-production application where speed was more important than tool flexibility.
posted by cardboard at 6:37 PM on August 31, 2009 [1 favorite]


A circular tunnel put limits on the number of lanes due to height restrictions on the sides. A square tunnel (or a rectangular one with squares bored out side-by-side) would have less wasted space.

Circle > Square wrt strength. Your bicycle does not have square tubes for good reason. Arches and domes are relatively simple, resource-efficient, and were invented millennia before square structures. Tunnels are best built using curved, ie. "circular", bores: much stronger, much safer, less costly, and longer lifespan.

It'd be better to drill a bigger hole or drill two parallel holes, than to build a square tunnel.
posted by five fresh fish at 8:30 PM on August 31, 2009


Screw this. I'm going to go slice some bread. With a whisk.
posted by iamkimiam at 8:31 PM on August 31, 2009 [1 favorite]


In England, 20p and 50p pieces are Reuleaux polygons. This is so that vending machines will be able to tell the coins apart entirely by their diameters.
posted by painquale at 8:38 PM on August 31, 2009 [1 favorite]


I think it is obvious that one can build a single-function machine that can mill a inch-square hole in a block of polyethylene using a carbide blade and constant scrapings-removal, maybe an air jet, maybe water to cool the block. And it'd eventually drill/scrape out a square, shallow hole. It is a Real Machine™.

I just don't see the point in demanding they actually build such an amazingly useless Real Machine™. The animation which makes it obvious how it functions is proof enough for me: you can indeed build a machine that will drill a square hole. That's a pretty cool discovery.
posted by five fresh fish at 8:48 PM on August 31, 2009 [1 favorite]


And by useless, I mean that this single-function machine is going to drill a 1" wide, 1/4" deep hole. Each. And. Every. Time. And only in polyethylene. And you'll probably have to change the blade a lot. Unless you have dire need of a LOT of 1" x 1/4" holes in polyethylene, there are far, far better solutions already at hand.
posted by five fresh fish at 8:52 PM on August 31, 2009


Honestly, whether this mathematical thing can actually be built into something to drill square holes... never entered my mind for a second.--vacapinta

I'm going to call you out on this statement. Your post clearly asks the question:
Can a drill be constructed which makes square holes?

It doesn't ask if it can mathematically or theoretically be built.

....not what it says on the tin.
posted by eye of newt at 9:03 PM on August 31, 2009


adicopere--

*cough* spacetime is curved *cough*
posted by effugas at 1:38 AM on September 1, 2009


This is even more of a non-sequitor at this point, but I messed up the link in my previous comment. Here is the turbocharged barstool promised above.
posted by mosk at 1:54 AM on September 1, 2009


Don't laser-cut leather though, because the smoke stinks like nothing you ever smelled before.

It's not so bad. It smells about the same as any other piece of burning skin and hair.

(What?)
posted by rokusan at 4:51 AM on September 1, 2009 [1 favorite]


How Round is Your Circle isn't that new. I've had a copy for almost a year. It's pretty great, but you'll definitely need some math to get the details. Linkages, non-round rollers, balancing devices, and more.

YouTube channel and link to main page of official website.
posted by DU at 5:00 AM on September 1, 2009 [1 favorite]


As others have already said, lasers are in fact very, very good for cutting wood, and that is why at your local chain hardware store you can now buy intricately cut fretwork pieces that have those burned-looking edges.

Mitheral I'd like to add a laser to my cnc router at some point in the future capable of cutting up to 3/4" plywood. Besides the great reduction in waste because of the elimination of a physical cutting head a laser doesn't apply any side force to the material meaning clamping needs are greatly reduced to the point of almost being eliminated.

I recommend you join www.cnczone.com if you haven't already. Regarding this particular project, it's a fantastic idea in theory to have a CNC machine with swappable laser/router(/RepRap/plasma torch/vinyl cutting knife/waterjet/sewing machine/cake frosting...) tool heads, but in practice laser tubes need to be quite big, about the size of a fluorescent light tube, and that works against head-mounting to the point that you're probably best off just building or buying another machine designed specifically for the laser. This of course has the side benefit of you being able to use both machines at the same time.

In most laser engraving machines the tube sits in a fixed mount and the laser beam is brought to the work by a series of mobile mirrors. However optical fibre of sufficient reflective quality might work.
posted by aeschenkarnos at 5:55 AM on September 1, 2009 [1 favorite]


that ...
is. so. cool. and i like the rounded edges : )
posted by msconduct at 5:57 AM on September 1, 2009


The main reason I want a garage someday is so that I can have my own CNC equipment.

I am such a guy sometimes.
posted by rokusan at 6:36 AM on September 1, 2009


While we are talking about linkages and mathematics: Square a complex number with a mechanical linkage
posted by DU at 6:21 PM on September 1, 2009


My father had a drill that drilled a circular hole, but after the initial hole was drilled, the 4 corners of the square were cut out and the wood forced to the centre (to be chewed up by the drilled) by right-angular pointed chisels. As I remember, it would amazingly well on plywood, though required a little more pressure to do the chiseling.
posted by Kickstart70 at 6:29 PM on September 1, 2009


These. Best used in a drill press.
posted by five fresh fish at 8:30 PM on September 1, 2009 [1 favorite]


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