## Compound Angle Box Joints

This is a practice piece for a larger project.  I wanted to make a tool tote like the one Roy Underhill carries in the introduction to “The Woodwright’s Shop”.  There is a description of the tray in Roy’s book “The Woodwright’s Apprentice”. His example is butt jointed and nailed together, but I thought it would be nice to do the tray with box joints and glue.  Thus started a journey into trigonometric hell.

Practice Piece

The sides of this piece are 15 degrees from vertical (75 degrees from horizontal) which is close to Roy’s slope of 1 1/2″ rise over 5 1/2″ run.

The only other reference I had for compound joinery was a section in Tage Frid’s book “Tage Frid Teaches Woodworking, Book 1: Joinery” on hand cutting dovetails in a similar situation. Not for the amateur woodworker and difficult to follow.

Strange things happen when you slope the sides of a box.  All the angles change and the side edges are no longer parallel.  People who install crown moulding are familiar with this.  I used the Butt Joint calculator at www.pdxtex.com/canoe/compound.htm.

To get the side and bevel angles needed for the project. It is easier for me to think of these angles as offset from vertical (90 degrees) so I entered 75 degrees as the side slope.

Compound Angle Calculator

The table saw has it’s blade tilted to the calculated bevel angle (3.84 degrees) and the miter gauge tilted to the calculated side end angle (14.51 degrees from 90 or 75.5 degrees).

Cut the first edge with the miter gauge in the left hand gauge slot. It helps to label the faces as the small bevel angle is small and not obvious. The narrower face goes towards OUTSIDE of the pyramid. For my right tilt saw, the piece being cut off in this photo has it’s INSIDE face up in this photo. The next piece, on the left of the blade, has it’s OUTSIDE face up in the picture.

Compound Cut

Now rotate the miter gauge 180 degrees and put it in the right hand slot. Flip the board over and make the second cut. The piece being cut off now has it’s INSIDE face up.

This method does not waste any wood, but every other piece has it’s face side reversed which may be a concern if you’re matching grain.

After all the pieces were cut out I ran them through the saw a second time with a stop block clamped to the miter gauge to ensure they were all the same width.

The final step in fabricating the four sides is to tilt the saw blade to the slope angle (15 degrees in this case) and bevel the top and bottom of each piece. I used the table saw fence to guide this, but watch out for kickback.

Second Compound Cut

If the butt joint angles are cut correctly on the table saw, a straight edge held parallel to the top or bottom will show no gaps across the junction of two sides.

Joint Alignment

To dado angled box joints exactly parallel to the slanted top and bottom edges, the work pieces have to be held in the jig in the position they will occupy in the finished assembly.

I made two complimentary spacer blocks, one for the right edge of the work piece, and another for the left.  I first glued up a 3 inch thick blank from four pieces of 1×6 pine. This was trimmed and planed square.  Then I laid out the lines for the necessary slopes all the way around the block.

Angle Block Layout

The next corner of the block.

I found it was easier and more accurate to lay out the lines by calculating and measuring rise over run rather than use a protractor.

Second Side of Angle Block

This is the opposite corner of the block.  The layout lines go all the way around.

I made several of these blocks before I got the angles dialed in right.

Third Side of Angle Block

The fourth corner of the prepared block. The next step is to slice the block along the layout line.

Fourth Side of Angle Block

A Sketchup model of the jig spacer block.  Angles for this 15 degree project are 3.8 degrees on the long side, 14.5 degrees on the short edge.

The dimensions shown are approximate due to Sketchup limitations.

Sketchup Screenshot

This shows me and Henry Disston dividing the block along the layout line. It’s easier than it looks.

For a good example of how to do this see www.pbs.org/woodwrightsshop/video/2800/2810.html where they slice veneer off a walnut block by hand sawing.

Splitting the Angle Block

Here the two halves of the block have been smoothed, and pegs added so they will plug into my box joint jig.

Note the orientation. The block on the left will go against the jig on it’s square face. The block on the right plugs into the jig on it’s sloping face.

Two Setup Blocks

A view showing how the sloping faces of the spacers lay against the jig. One spacer tilts out 3.8 degrees and slopes 14.5 degrees left, the other tilts in 3.8 degrees and slopes 14.5 degrees right.

Side View of Spacer Blocks

The dado stack has to be tilted to match the side angle. This aligns the slot with the top and bottom surface of the work piece. For this 15 degree side slope project, the angle is 14 1/2 degrees off vertical.

An additional complication is, now that the dado is angled, the slot will be slightly wider than the stack width. Box joints depend on the slot being exactly the same width as the pin, so the pin size has to be increased to match. For this 15 degree project, I added 0.012 shims to the dado stack and increased the pin cycle by 1/16 inch. It came out pretty close.

Wixey out the Angle

Finally the jig with spacer is ready for duty. Here one of he blocks is plugged into the lead screw jig carriage, the work piece and a backer board are clamped to the spacer and I am pushing through the dado.

Note the masking tape throat plate. The jig itself provides a throat for the Dado set, the tape just keeps down the sawdust.

Clamping the work piece at the necessary angle is difficult. I used tapered shims to get a straighter purchase for the clamps.

Clamping the Workpiece

Since the stacked Dado set cuts a square bottomed slot, but the edge parallel fingers require a trapezoidal hole, there is a small triangle of material that must be removed from each of the slots by hand.

Here I am knifing the edge of the triangular area.

Knifing the Slots

The small side of the triangular areas can be sawn.

Sawing

One of (many) practice pieces showing the small triangular area at the top of each slot that must be removed. Here I have defined the triangle using a straight edge and utility knife, also the small side has been cut with the dovetail saw.

Now to remove the waste from the triangular area with a paring chisel.

It might be possible, if thinner stock is used, to build a fixture and do the clean out with a 14 degree dovetail router bit. If I had to do a lot of these I would investigate but it doesn’t take long with a sharp chisel.

Paring the Slots

Not a bad dry fit.  The material is cupped a bit which left some spaces but I think it will pull together with sufficient glue clamps.

The sloped sides are going to be a problem on the glue up.  I will make some 15 degree cauls to keep the clamps from sliding off, also will use strap clamps.

Dry Fit Practice Piece

Finished Compound Angle Projects

This is the finished Roy Underhill Memorial Tool Tote created with the compound angle box joint jig.

First Tool Tray

Close up of the compound miter box joints on one end of the tool tote.  I don’t have all the cool hand tools Roy has so this project was built with machines.

Corner View

Detail showing how the handle is mortised into the end pieces. Just like Roy’s.

Handle Detail

This is a smaller tray in Cherry.

Tool Tray in Cherry

This was the last one I made, in Yellow Pine from Home Depot stair treads. The bottom is nailed on the sides, I covered up the finishing nails with copper carpet tacks.

Yellow Pine Tool Tote

1. Pine is pretty much all we get at a reasonable price in Australia but the cherry looks excellent.

2. Cool. I found this looking for hints on an interesting compound angle box joint along the edges of a rectangular box, and I think your tricks would work–it looks like you’d keep the same angles and spacers, but you cut your boards square in the first step.

I wish I took a picture — the canted fingers were really dramatic. Set your test piece on one of the sloped side, and imagine the top and bottom off square to that side.

• There aren’t any “square” cuts. The secret to cutting the fingers is to hold the work at the angles it will have to assume when assembled. Then make the cuts. Not easy figuring out those angles though. woodgears.ca has some thoughts.
There are ways to do compound angle butt joints using an angled block on a table saw, and a few on doing dovetails by hand at angles but I never saw anybody else do box joints.

• I meant that the finished work/box that I saw was square, so the initial full cuts across the stock boards are square, but the fingers were canted (upwards, I think?) with respect to the horizontal plane. Your fingers are horizontal when your box is sitting normally, but if you tip the assembled box up to hold one of your joints vertically, then the fingers on that joint would also tip upwards, and the joint would look somewhat like the box I saw. (the angle between the walls in the horizontal plane when your box is tipped up wouldn’t be 90 degrees anymore)

3. Here’s a video where they call doing your compound angle box joint on a right angle a “twisted box joint”: https://www.youtube.com/watch?v=mzQOmQ5RrgI

The beautiful old scientific instrument storage box I saw was about 9x12x18 tall with 3/8″ walls, and the fingers were about 1/4 to 3/8″ wide.

4. I’ve seen structures with angled joints as you describe. But keep in mind, if the fingers end up crossing the grain they will be weakened. I have a Tage Frid book where he does compound angled dovetails, he goes to a lot of trouble to ensure the pins and tails align with the grain. There are a number of youtube posts on making compound angle dovetails. All are cut by hand. I don’t see any way to do compound dovetails with a router.

• I took some pictures and posted them at https://drf5n.wordpress.com/twisted-box-joint/ — they are not dovetails, but compound parallel-sided pins that could be cut with a dado and trimmed out with chisel (or as I suspect, cut out with a slitting saw ground with an angle profile) I think you could do them on your setup with a plain 10 degree fence, and a plain 10 degree tilt on your dado.

There are indeed a couple cracks where the 10×10 compound angle of the pins crosses the grain, and the glued joint pulled the grain of the pin apart a bit.

5. I think you’re correct, and would need the special ground blade only for the cuts on the top piece. I finished the angled seats with a paring chisel, it’s hard because the chisel has to be held at an angle.

I wonder if there’s a reason for doing the case like that or was it just decorative?

6. Maybe since the lifting handle is on the top / a side with the joints, they might like the twistedness to add a little wood so you aren’t relying completely on the glue. The panel would have to slide a bit forward or out to come apart, meaning that two joints would have to fail before it would drop the instrument.

I got the case open and inside are three small straight-peg storage boxes–one a sliding pencil-case-like thing, and two open-sided sample bottle racks with 6 round 1″ holes on top. A couple plastic “Leitz Wetzler” sample bottles were strong hints that it might be an old Leitz Wetzler Microscope case.