Category Archives: Splay Leg Stool

Splay Leg Stool Assembly

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The last thing I’ve left to explain in the construction of a splay leg stool is finding the length of the rails which connect the legs on all four sides.

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There’s nothing like the moment of assembly to find out if all the careful calculation and drawing work was correct. These splay leg assemblies come together all at once, with all the joints tightening progressively.

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Everything looked like it was going so well, and then the legs bottomed out in the joints and there was still about an 1/8″ of travel left in the rail tenons for the joints to come together. Like I said, moment of truth. The problem then came down to finding out where I had made the error.

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At first I was dumb, and didn’t think about the relationship between the leg length and rails. For every inch that the rail tenons come together the leg tenons have to move into the mortises about two inches…

But like I said, dumb, right? Out came my little saw with no set to try kerfing the joints on the legs to get a bit more travel. I wasted about two hours trying to get the rail tenons together, maybe .020 inch at a time.  Kerfing is a great technique for getting nice tight joints, but the shoulders for the leg mortises needed to move back something like a quarter of an inch. where did I go wrong?

Leg Length Drawing

It was in my assumption that the distance of the rails was measured along the centerline of the top and bottom edges, and I had the drawing all along that showed how I was wrong, but didn’t see it. Funny how that happens. Effectively I cut the rails too short between the tenons. Rather than re-cut new rails, it made more sense to make the legs a bit shorter at the tenon shoulders. Thankfully this is a correctible problem, I’ll just end up with a stool that is a tiny bit shorter than I had intended.

The above excerpt from “How to use the Sashigane” Shows another small stool, with the length of the rail transferring directly down from a elevation view to the view of the rail from the top. Notice how the length points are along the edge? Yeah.

Leg Length

In my own drawing I had the correct lengths, but thought that the measurement point once the stool was folded up along the ground axis on one side was now the center line. I failed to reference the corresponding length of the edge on the other half of the rail. If I had, I would have found that the length does not change along the bottom edge of the rail in either side of the view, elevation to fold-up.

Difference in Leg Height

By placing a trace line on the center line and transferring it up to the fold out view I was able to find how much too long my legs were, a whopping .276″.  There was nothing to it now but to disassemble the stool and re-cut the leg tenons.

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But doing that was not simple either. Seeing as all of the joints tighten together as once, you pretty much need to pull all of the joints apart at the same time. The solution? The humble wedge used under the rails, constantly providing pressure to lift the leg assembly from the top as the rails were tapped apart with a hammer.

In a way I’m pleased this happened, because I ended up understanding the drawing relationships better.

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I had already chamfered the edges of the legs, so it made laying out the new cut lines difficult, but not impossible, and this time the stool assembled properly. It could still use some kerfing on the joints to get a perfect seamless fit, but that can wait until the doug fir I made this from will dry out a bit, as I resawed the material from a timber framing beam off-cut that was still green.

I was looking for a challenge in taking on this stool build, and it doesn’t surprise me that I made some mistakes. In any woodworking endeavor that is often the case, and it equally takes skill to figure out how to fix the problem that was unforeseen. Don’t give up when you run into an obstacle like this! Its something we all learn from, and it will not be the last time I learn from my mistakes more so than if everything went perfectly to plan.

Cutting Compound Angle Mortise and Tenons

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Is modern digital technology running rampant in your life? Grab a saw! Join me for a little work and find out if your mind has been colonized by a corporation.

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I finished the stool yesterday, so time to work through the rest of the problems associated with making a splay legged stool. Its a good thing that I’ve waited to post about this until finishing, because I found a few mistakes I made that were very instructive in understanding this project, which I’ll go into more detail with on the final post of this series detailing the final assembly.

The compound angle of the mortises meant that chopping with a chisel would have presented some great difficulties, so I started by drilling the waste with a brad point twist drill. I used the layout lines on the sides and a straight edge placed on the side for visually aligning the drill.

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Just as you would for chopping with a chisel, drill half way through from both sides to reduce the chance of drilling waste outside the cut lines.

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The table mortises were first layed out on the bottom using measurements from the center lines of the board, with the lines transferring up on all four edges with the common 3.5/10 slope to the top. Because the mortises were too far in to sight accurately I used a bevel gauge placed at 45 degrees in plan to gauge the angle for the drill and its alignment. In this case the angle for the drill, because it is at 45 degrees to plan (top view) uses the displacement multiplied by the square root of two, working out to about 4.9/10 for the angle to set the bevel gauge to.  Why the square root of two? I’ll let you figure that one out, its very, very common in dealing with slopes that are a regular 45 degrees in plan.

To pare the surfaces of the mortises in the top I made a guide block for the chisel at the common slope, which applies to both the end grain and side walls of the mortise. One block to pare them all.

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I tried using the extra leg I had cut as a guide block for the mortises on the legs but found it faster to simply sight along the edge of the leg, and used a big timber framing chisel.

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Cutting the tenons was very special for me because it was the first chance that Mark has given me to try some of Yataiki’s saws. I used a 240mm ryoba for all of the cuts. This saw was very good, to put it mildly. My saws are all mushy disposable blade type, so coming from that to a saw like this is a quantum leap, and I joked with Mark whenever he asked how it was going that I had only broken off a couple of teeth. That is a real concern with lending someone a good saw to use, its no small matter, you don’t just hand a saw like this over lightly, and I greatly appreciated the gesture on Marks part to let me use this tool.

The saw was very thin, light, and finely set. Easy to use one handed, and really did all of the work without me pushing it through the cut. For the first time I felt like I was really experiencing new dynamics of the saw in the cut.

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Should you run across a saw with these Markings…

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Treasure it dearly.

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Yataiki gave this saw to Mark when he was teaching in Iowa for making charcoal for the forge and asking doing things like counting the number of teeth on a saw.

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It has some history, as the staining and hammer marks from hizumi will attest.

As an aside, I’ve been meaning to write a post on Marks hizumi hammers, but have been holding off because I don’t want to be too proscriptive about which hammer is the correct one for a particular task. What is important, besides the weight of the hammer matching the thickness of the plate, is the shape of the cross peen edge. And to that end, its easier to describe the correct shape and size of the mark it leaves than the degree of radius on its edges. Measuring the ghosts of the marks on this saw shows a cross peen mark about six millimeters long and one millimeter wide, an ellipse.

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The yoko-biki (cross-cut) are nice and slender little daggers, really well proportioned.

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The tate-biki are likewise pleasing to the eye.

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My normal method of ripping tenon cheeks is with the piece of wood held vertical in a bench vise, but I found the teeth of this saw too sharp and aggressive to handle the angle of cutting uphill to the grain. The alternative is cutting downhill with the piece held horizontally. The saw horse I’m working on is a bit low for this task but It worked nicely, with the advantage of being able to freely orient to the best light from the south facing windows.

Getting the chance to use this saw was a real eye opener for me. I knew my disposable blade saws weren’t that great, but the positive difference is almost unquantifiable, and I find myself hoping to buy, perhaps not a totally handmade professional grade saw, but something with decent steel that I won’t feel too bad about sharpening on my own. The world needs more saws like this!

Splay Leg Layout

Splay stool elevation and leg foldout

Today we take a closer look at laying out the mortises in the legs of the splay leg stool. Remember that previously from drawing the side elevation the view has been folded up along the ground axis to represent the faces of the leg as truly flat to the 2D plane of the drawing, and then unwrapped so that all of the faces of the leg can be shown at once.

Starting with the basic slope of the stool at 3.5/10 I was able to determine chu-ko slope from dividing the basic unit triangle, forming the slope that the foldout is drawn at, 3.304/10. This is the angle that the bottom of the legs are cut at, as well as the angle that the mortise travels through the leg.

There are no right angles here, even the top and bottom of the mortises have a slight angle, sho-chu-ko, but well see to that in a bit.

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With a non base 10 unit system of measure converting from decimals of and inch to fractions is made much simpler by dialing in the measure on my dial calipers and seeing where it hits on the scale of the sashigane. One of these days I’ll switch to shaku  and metric, but until then I continue with this madness.

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In practice the angle for the bottom cut of the leg looks like this on the sashigane, with one arm holding 3.304 and the other the base unit of ten.

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You need to mark this same angle a whole bunch of times so it pays to fix a bevel gauge to the same angle. I like this stainless Shinwa sliding bevel!

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And to help fix it in the mind you can compare directly to the drawing. Or if the drawing is closer to scale you could take the angle directly from the drawing.

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I took a moment to examine the relationship of the faces of the leg to their orientation, and found that you have to cut two sets of legs. The ones that diagonally oppose each other are the same, all of the angles are opposite for the other pair.

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I never truly understood the elegance of center line layout until starting on this saw horse. Edge rule is fine for orthogonal work (at right angles), but when there’s compound angles your measurements need to be referenced to the center line. For instance, because both the face and edge cuts of the rails are miters the lengths you pull from the drawing are along the center line, not the edge. Suddenly the beauty of this system becomes very clear.

For the placement of the mortises I measured along the center line as well, with some of the measurements easier to transfer directly from my dial caliper.

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With one leg marked I used the edge of my wooden straight edge as a story stick, transferring all of the marks to the stick so that I didn’t have to spend time making all of the measurements again and again. In Japanese this is known as an ‘idiot’ stick. Call me an accurate idiot then…

Sho-chu-ko

For the angle of the top mortise the smallest division of the unit triangle is used, sho-chu-ko. This is the tiny little line on the bottom right of the triangle, forming a new slope of .361/10, or an angle of 2.067 degrees. This one I didn’t lay out directly with the sashigane because the actual angle needed is ninety degrees to the edge of the leg plus or minus sho-chu-ko.

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Functionally its two degrees, so I used a protractor and set another  bevel gauge to the resulting line.

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The width of the mortise is measured along the sho-chu-ko line, not perpendicular to the edge of the leg. That little detail held me up for quite a while, and I had to go back and fix my drawing so that the mortises did not interfere.

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Compound angle joinery is improved with a little beer.

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A two legs from any side of the saw horse are mirror opposites. I’m showing you the nice looking layout, not the ones with lines scribbled out everywhere…

Next is the layout on the rails and top, and then finally I can start drilling the mortises and cutting tenons! I hope this inspires someone else to take on the challenge of figuring this out.

Those Legs Ain’t Square

Splay Legged Stool

Starting now on a new build thread, a Japanese splay leg stool. Why a stool you ask? A splay leg saw horse is in the series of exam challenges for a Japanese carpenter after a ‘hopper’, introducing the fundamental concepts of working with compound angles that are necessary for the complexity of understanding and laying out hip roof framing. I merely chose to make a stool as opposed to a saw horse because horses are best made in sets of two, and a stool takes far less lumber. Plus, I’ve felt the need for a short stool to sit upon while sawing lumber (oddly enough two identical stools would be better for this task as well, but one suffices).

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I’ve cut a roof in the past where I ran into some of these compound angles and used several modern western books to understand the layout, which has gotten me by just fine. But the Japanese methods for some reason just make more sense. And I want to cut timber frames inspired by Japanese structural joinery.

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To avoid some awkward geometry where the rails meet the legs the footprint of the legs are made square to plan (the view seen from above). As a consequence of the leg being splayed, tilted at an angle in two axis, is that the cross section of the leg becomes diamond shaped.

So, how does one figure out the right shape to make the leg? Lets pull back a minute for a bit more introduction to rise/run and the hopper shape.

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Here from the Japanese text “How to use the Sashigane” is a picture of two different hoppers, a mitered hopper and a butt edged hopper. The geometry of this form applies to a splay leg stool as well, which you might come to see as a hopper turned upside down.

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On the left page is the introduction to slope expressed as rise/run, just as you might use in describing a roof in the west as 6/12, or 12/12. For a base unit run of 12 the roof rises, or displace, a given amount, and the pitch of the roof that keeps the rain off your head is defined. In the rest of the world run is defined with a base unit of 10. So in the case of the hopper in the photo above for a base unit of 10 it has a displacement of 3, or a 3/10 slope seen in elevation (side view).

Given that basic relationship a triangle is formed, with the two right angle sides defining the hypotenuse (seen on the right page above). In the Japanese system each of the sides of this triangle is given a name, ko , ko , and gen 玄.

By further dividing the unit triangle the slope angles for compound miter cuts can be found. The first division, cho-gen, is made by drawing a line perpendicular to the hypotenuse (gen) which intersects with the right angle corner of the rise/run. In the text above they help you out by assigning cho-gen a square shape. Knowing this length allows you to form a new triangle that gives the face cut angle on a hopper, or the angle that a rail meets a leg for the stool that I’m making.

By using the base unit of 10 on one arm of the framing square and the cho-gen length on the other, a new triangle is formed and you descend down the rabbit hole of ki-ku-jutsu! Fun times! The sashigane is your calculator, no math required. Similarly the edge miter angle for a hopper (or the edge miter of a rail meeting a leg) is found in the same unit triangle with the division of the hypotenuse by the cho-gen line.

TAJCD Volume 2 cover

Want to know more about this without searching for obscure Japanese carpentry texts? Chris Hall has published a great series of texts here. I’ve only bought the second one, and its helped me tremendously. Help a brother carpenter out and send him some love (and by love I mean money).

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This page shows one good method (far from the only way) to find the correct shape for the leg of my stool. What they’ve done is folded the sides of the leg out like opening a cardboard box and layed it flat to represent it accurately in two dimensional form.

Using the width of the leg along the ground a square box is drawn. Next a line is drawn diagonally that represents the outside arris (corner) to the inside arris. By taking the width of the leg perpendicular to its length with a compass and swinging it down to where it intersects the diagonal the first of the corners can be defined. See? This shit all boils down to basic geometric concepts and you should be able to fill in the rest of the leg cross section from there. The photo above also shows the method for laying out the rail mortises so that they do not interfere, as well as an interesting way to find the angle of the top and bottom edges of the mortise (sho-chu-ko, a further division of the unit triangle).

But how does one draw the foldout view of the leg at the right angle in the first place? It is in fact not the same as a simple elevation view, remember that in elevation the leg is leaning away from you, so the true lengths of the joinery along the leg cannot be taken directly.

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Here is the elevation view, and they’ve done something really cool. Can you tell? They’ve folded the whole drawing on one side up along the ground axis so that the leg face is represented truly flat/vertical! If you were sitting on the ground in front of the stool its like leaning the whole stool towards you. In elevation view the leg is defined by the common slope (3.5/10). By projecting a vertical line along the slope of the leg a point is chosen along the slope and swung with a compass up to meet the vertical line. Because any given point remains consistent along the vertical axis you can now draw the face of the leg so that measurements along its length are accurate.

Notice that the leg is now at a new slope. If you were to take your sashigane and measure this new slope, what would you find? Its our old friend Chu-ko slope! Okay, too much exclamation, but this unit triangle shit is pretty cool. This is the same slope used to draw the foldout view of the leg. There’s more important detail to the above drawing, but I’ll save that for when I get to the rail tenons.

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Back in the real world I became a little suspicious of the accuracy of the straight edge on my sashigane, must have dropped it again…So I made a simple wooden straight edge long enough to draw the center lines on my stool legs, about 24″ of vertical grain doug-fir, the same lumber I resawed for the stool.

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The two halves are cut from one piece, book matched, and match drilled for dowels that are glued in one half. The dowel is a good tight fit and allows the edges to be planed together.

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By planing them when they’re together any deviation from straight is doubled when viewed with their edges together. Its a simple technique and beautifully accurate. Its accuracy that you can really trust because you always have a reference edge to check it against, no wondering how straight it is, check that shit and be sure. The side with the glued dowels is the reference, in practice only the other half is used to check flat and draw straight lines.

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I used the same method I explained above to find the cross-section directly on the end grain of the leg, and inked a line on the faces to show how much material to remove. In order to know how close to meeting the other edge I was while planing I used a pencil to darken the wood. When the pencil graphite is gone you’ve planed out to the corner.

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Five legs (one spare for when I fuck up), ready for layout, a post for tomorrow. If you think this was complicated enough prepare to join me further down the rabbit hole.