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.
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.
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.
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!
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.
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.
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.
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…
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.
Functionally its two degrees, so I used a protractor and set another bevel gauge to the resulting line.
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.
Compound angle joinery is improved with a little beer.
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.