How do I cut a mortise and tenon on the CNC: round the tenon or square the mortise?

The problem

A pocketed mortise always has rounded corners with the radius of the bit. A tenon cut flat on the table (profiled out of sheet stock) has square corners in plan view. One of the two has to change, or the joint will not close.

Three workable approaches

1. Relieve the mortise. Add dog-bone or T-bone fillets to the mortise corners with Create Fillets, and leave the tenon square. This is the fastest route for sheet goods and for through tenons cut flat. A published CNC joinery reference recommends the simplest version: use the full stock thickness as the tenon thickness and cut the mortise with dog-bones or tees, so no part ever has to be stood on end. The relief shows on a through joint unless the T-bones are placed where the shoulder covers them.

2. Round the tenon. If the rail can be clamped vertically in a fixture off the edge of the table, the tenon can be profiled from the end with corner radii that match the mortise. The same reference describes this as the way to copy a traditional joint when relief cuts are not acceptable. Without a fixture, a published router tutorial simply eases the tenon corners by hand with sandpaper, a chisel or a knife until it slips in.

3. Round the mortise in the drawing. Draw the mortise as a slot with fully rounded ends (radius equal to half its width, using a Normal Fillet) and shape the tenon to match. The joint then has no relief holes at all.

Steps for approach 1

1. Measure the tenon stock with calipers and draw the mortise rectangle to that size.
2. Add T-bone fillets on the two short ends so the shoulders hide them, radius at least the tool radius.
3. Cut the mortise with a Pocket toolpath, or an inside Profile for a through mortise.
4. Cut the mortise first, then sneak up on the tenon. Cut a short test tenon in the same stock and adjust the profile Allowance Offset in small steps until it goes in with hand pressure.

Pro tips

• No fetched source gives a universal clearance number for this joint. Test on scrap of the same board.
• Leave room at the bottom of a blind mortise for glue.
• See the entry on dog-bone versus T-bone fillets for placement.