I found myself in need of a roughly cubical wooden frame the other day.
There are a lot of ways to fasten three sticks together to make a corner:
And in the end, I did end up using something like the above. But being the somewhat-obsessed-with-symmetry-and-patterns person that I am, I wondered if it would be possible to construct a corner joint where all three parts have exactly the same shape. The simplest “joint” of that kind is just three sticks:
Obviously, this “joint” won’t stay together without help, but we’ll address that later on. In my case, I needed the frame to extend to the outside edges of the cube (so that I could fasten some sheet metal over the frame). That’s easy to do with this geometry; just widen the sticks and cut a notch for the joint:
But there’s still that pesky empty cube in the corner. Is there a way to eliminate that without losing symmetry? It turns out that there is:
This isn’t a practical joint. It barely holds itself together, and it’s very fussy to cut and fit (and, if you look closely, you can see that it’s easy to break off one of the sharp triangular tips of the pieces). But it got me thinking: as impractical as it may be, it could nevertheless serve as an étude.
In music, an étude (French for study) is a composition whose purpose is to help build technical proficiency. Études are not meant to be performance pieces, although in a few exceptional cases, such as Frederic Chopin’s piano etudes, they have made their way into the performance repertoire.
Other fields of endeavor have similar practice pieces: chess players study standard openings, Japanese martial arts have their kata. The sequence of moves in tàijíquán can be thought of as a single long, extended étude.
Of course, woodworkers have…well, not much. There’s the Gottshall block, and Chris’s recently republished Dovetail a Day exercise. (Gary Rogowski has advocated something similar with his “5-minute Dovetail” regimen, although in his case it’s more of a warm-up stretch than an extended exercise.) And I’m looking forward to LAP’s new Charles Hayward book, as I suspect that it may contain some exercises along these lines.
But that’s about it. For whatever reason, the concept of standardized practice exercises doesn’t get much airplay in the modern woodworking world. One can argue that woodworkers want to make “real” things, and not just practice pieces, but the same argument applies to the other activities mentioned above: musicians want to perform for a real audience, chess players and martial artists want to face real opponents, etc.
So what’s the deal with woodworkers? Do we need a library of standard woodworking études? Would anyone do the exercises?
In case you feel the urge to duplicate the joint in the photo above, here is a procedure that I’ve worked out.
You’ll need three sticks that are about twice as wide as they are thick, with the end in which you’re going to cut the joint nicely squared off. You will also need a thin shim, about 1/16″ thick. Set your marking gauge to the thickness of the sticks, and on each stick scribe a line up one face, across the end, and down the other:
(I’m showing two views of the end of the stick, so that you can see both sides.) Make sure that you note which edge of the stick you’re referencing your measurement from; in this illustration, I’m referencing from the upper edge.
Now reset the gauge to the thickness of the shim, and scribe a line all the way around the end of the sticks.
Repeat with the gauge set to the thickness of the shim plus the thickness of the stick:
And finally, with the gauge set to the thickness of the shim plus the width of the stick:
Scribe two 45° diagonal lines as shown:
Note that if you’re ambitious and want to build an entire cube, the joints at each end of a stick have to be mirror images of each other, or else the cube won’t go together.
Use a saw and chisel(s) to cut a notch in each piece, from the edge that you referenced above, as if you were making a lap joint. You want this to be a good snug fit.
Remove the triangular waste adjacent to the notch:
I find that the simplest way to do this is to lay the stick on its side and cut down with a chisel, removing a big chunk at first and then sneaking up to the line. Err on the side of caution here; you’ll be fitting this line against its mating piece later, so you’ll want a little extra meat to work with.
Now remove the other bit of triangular waste:
The easiest way to do this is to mount the piece in a vise, end up, and split the waste off with a chisel. Since the cut is along the grain, it splits off easily (maybe too easily). Again, leave a little bit of waste to remove later during fitting.
Mark the pieces on the side and end so that you can keep track of how they go together. I used a simple marking scheme:
Finally, fit the pieces together in pairs, gradually paring away the remaining waste material until the pieces fit together closely. (You can cheat a little and make the fitting easier by slightly undercutting the two interior triangular faces.)
Once the pieces have been fit together to your satisfaction and you’ve assembled the joint for good, you can plane off the 1/16″ extensions, the purpose of which was to help prevent the unsupported triangular tips from breaking off, much like the “horn” on a mortise-and-tenon joint serves to keep the end of the mortise from blowing out.
This joint sort of holds together with friction, but it won’t stay together without glue (or pins). I’ve come up with a modified design that ought to interlock much more tightly:
Unfortunately, I have yet to figure out a decent way to cut it (without resorting to a CNC mill). The experimental failures are currently littering my shop.
An étude for another day, perhaps.
EDIT: Bronzy935 asked about how to pin the joint; I’ve done something like this before (using screws), and it’s surprisingly sturdy:
21 thoughts on “Études”
Checkout joint on X-Hocker Stool
similarly, could make this cube with sticks that are triangular in x-section. only have to 3-side ’em! not sure the joint would lock any better though. see http://www.johnrausch.com/PuzzlingWorld/chap07.htm
Now cut that joint by hand…
Ron Herman has an etude as the basis of his “Joinery Challenge” DVD. It’s one project (a frame) with nine joints. Some of them are not hand tool oriented, such as pocket screws. I’ve been reworking the specs to focus on hand tool joints.
Thanks for reminding me. I don’t have the DVD, but I do remember seeing something about that.
Steve! How nice to “see” you again!
Yea, was wondering where he disappeared to. Enjoyable post.
I’ve been busy…
I do plan on dropping by Braxton Brewing sometime Friday.
Back when manual training was part of (at least some) school curricula there were often a series of exercises, referred to as Sloyd. There may be some old Sloyd manuals scanned online. Maybe a project for Lost Art Press. Your project looks to be tending toward what Hayward called a “showcase joint” or “3-way miter.” Hayward’s “Woodwork Joints” describes it, as does Yeung Chan’s “Classic Joints with Power Tools”. A friend did a couple of end tables utilizing them as a school project, with a lot of head scratching and improvisation.
I hope the joint is easier to cut than Chopin’s Etudes are to play. Whew.
A very nice study in the wood you have chosen, looks great. For anyone wondering, tàijíquán is also known as Tai Chi Juan, or simply Tai Chi. Many do not realise that Tai Chi is a martial art at all, after seeing 90 year olds practising in the park. They are doing their étude, don’t mess with them!
Since the Chinese influence has already been discussed, why was a 3way miter not considerd in this application?
I was thinking the same thing, though it’s far too challenging to do merely as an exercise. To cut a joint like that entirely by hand would take me forever. Just laying it out would take me forever. For those who wonder what we’re talking about, I found this on Youtube: https://www.youtube.com/watch?v=YkDQ5eFW_rQ
Remember that the motivation here was to see if a joint could be made where the three pieces were identical. A Chinese three-way miter is symmetrical from the outside, but the inside is anything but symmetrical.
Where would you locate pins?
I added another image at the end that shows where to put pins.
‘The Essential Woodworker’ book by Robert Wearing contains several “standard woodworking etudes.” I combined these with some recommended by Paul Sellers to make a list of 10 that hangs over my bench. It’s been a while since I practiced them, and I am missing a few, but the three I can remember are:
1) Split a line
2) Plane a length convex
3) Plane a length concave
I can send you the whole list. They are very helpful.
Too bad we can’t post images here. I have an ongoing design exercise I’ve been fooling with that is very similar to this.
The pin version is sold as grid beam, among other names. http://www.gridbeam.com/ I have a set, handy for things where you want to take it apart and reuse it and prototyping. Right now, my monitor stand it made from it (part of it broke off, so something needs to hold the flat panel up), and my kids have made stilts and other things with them. They are 2×2 (so 1.5″ a side) with holes every 1.5″ on both sides, starting 0.75″ from the end.
William Fairham, Woodworking Joints, fig 57, Cross Rail and Upright Halved Joint, is designed for this. Not as pretty, but eminently functional. I used it to make a stick built shop cart. It can be adapted to make a 3 wqy jpint mid stick, as well.
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