Lower Shelf
The wedged tenon joints where the shelf passes through the shelf rails must be cut neatly and accurately. Start by edge-gluing two or three pieces of wood to get the required 13 1/2"-shelf width.
Next, cut four through mortises in the shelf rails. After marking their locations with a pencil, cut from both sides, drilling out the majority of the waste, and clean up with a chisel and file. The mortises must be square and neat on both sides.
While there are measurements on the plans that correspond to my table, there can easily be slight variances when you build. That's why in this case it makes sense to dry-fit pieces together temporarily with clamps, check for square, then take measurements directly from your assembled parts.
Next, measure the actual distance between the two shelf rails. This distance is the between-the-tenons length of the shelf. Remember to add 1 1/2" for the thickness of the shelf rails and 2 3/4" for the length of the tenons themselves to get a final length of the entire shelf piece. Cut your shelf panel to length and mark out the locations of the tenons directly from the rails. Use a bandsaw or jigsaw to cut away the outside corners.
In order to get a straight cut for the cutout between the tenons, use a jigsaw with a cutting guide clamped to the shelf. Or make this cut quickly and accurately with a plunge cut on your tablesaw. Set the fence the required distance away from the blade and raise the blade until it is just higher than the thickness of the wood. Mark the fence at the point at which the blade comes through the saw's tabletop at the front and the back. Then lower the blade and turn on the saw. Hold the shelf against the fence so the mark for the back of the blade aligns with the cutout for the rearmost tenon.
Carefully and slowly raise the blade while it's spinning until the teeth protrude through the top surface. Slowly feed the wood into the blade until the mark for the foremost tenon reaches the mark you made earlier on the fence for the front of the blade. Hold the board securely on the table and against the fence, then shut off the saw. Wait for it to come to a stop before lowering the blade. The saw blade is curved, so the cut will be arc-shaped. You can square it with a jigsaw or handsaw.
Dry-fit the shelf and shelf rails together to ensure that the shelf tenons fit through the mortises perfectly. Again, to prevent chipping during your test-fits, make slight chamfers on the mating pieces.
Next, cut the small mortises that go right through the tenons. These accommodate the wedges that hold the shelf in place. The best way to find their location is to mark the point at which the shelf tenons exit the rail mortises with a pencil line. Since wedges like this work best when they apply real force to the joint by pulling everything snug, you should make your wedge holes 1/16" inside the lines you marked. See the plans for details.
After marking the shape of the wedge holes, drill out the majority of the waste with a 5/8" Forstner bit and clean up the rest with a sharp chisel. To get the angled, outside faces of the mortises just right, cut a block of wood with an edge that's 3ยบ from square that you can clamp to the board to guide your chisel. Also, be sure to clamp a board to the bottom edge of the hole to prevent tearing out the edges when chiselling.
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