No, Lapped mitres are not some friends that have been attacked by an over friendly dog. These joints are a mixture of 2 different classes of joints. If you've been to any of my classes; I will have taught you about a number of classes of joints among these are the butt joint and the lap joint.
The butt joint is typically joining end grain to side grain. This makes the most weak glue up joint. But of course it can be reinforced. wikipedia has a few techniques. In fact most of your modern day furniture is made in this manner, with some real cool fasteners (A topic for much later). Now a mitre joint is a butt joint, but a decorative one. In fact, these are end grain on end grain joints, and definitely cannot be loaded very much.
The lapjoint, is nothing but 2 pieces of wood, overlapped and glued up, the good thing about this joint is that it is side grain to side grain, which is good for a glue up. This joint class has some fairly strong joints, but to really make them sturdy woodworkers of old learnt to cut out half the wood from each of the mating pieces and lock the 2 together. This would give the joint some support from the surrounding wood edges and make it way stronger, and hence gave us the half lap joint.
With that background, I'll continue to using the lapped mitre joints in frames.
This is frame build 1, I started with the toughest, as I usually do. What follows are descriptions and images of the techniques I use to cut half laps, tenons and even dovetails. (If you have any difficulty following my verbose rambling, please leave a comment)
Measuring and marking
Lapjoints are easy to mark, all you do is hold at right angles the 2 pieces that have to be joined and score the width of one on the other. There is no real need to measure. If you are marking with a pencil or pen, please please do remember to cut 1/32th inside the waste side. Don't forget to carry the line to all 4 sides of the piece. And then, finally mark the depth of the half lap joint.
Patience. Cut inside the line, unless you've used a scribe and even then, cut inside the line. Nothing is more frustrating than a joint that rattles.
There are many techniques for cutting a lap joint, the one I follow is a quick one and can go wrong if the grain flow has been incorrectly read.
Begin cutting to the depth on one side of the lap. Make your first cut to full depth.
Your second cut is now made leaving a gap of 1/8" to 1/4". The deeper the half laps, the more large the spacing of these cuts can be. For example, I'm cutting down to just 5mm, so I had to keep the distance pretty small. When you finish the second cut, tilt the saw slightly till the piece of wood breaks off. This piece will break off pretty much at the depth of the cut. And this is the reason why the distance is important, to much distance and there is too much material to lever and break. So err on the side of small distances.
Here is my lapjoint looking like a caterpillar, and no, the sawing wasn't slanting, these are the pieces that have broken off and are lying on their side.
After this, it's a quick matter of cleaning up the floor of the joint. Use the largest chisel that you have so that the floor is even at all points. Watch out for the grain flow. You don't want the chisel to go too deep while cleaning up.
Do the same thing for the mating piece
You should now have the perfect lapjoint. Now to make them lapped mitres.
As I said before the half lap, gives strength, and the mitre gives beauty. So make sure that you are cutting the mitre on the upperside :) yes yes, I know... but hey mistakes happen, and then I had to explain to the wife why I had some ugly ass frames.
Ok, So here's a look at what the 2 pieces should look like. As you can see, on the one side the half lap is cut at 45 degrees while on the other the entire piece is cut at 45 degrees, but the groove is made perpendicular to the edge.
The fitting of the joint is simple and because the joints are essentially halflapped they don't have that irritating habit of sliding around when you try to glue them up.
I do admit that this particular joint is a bit of an over kill for the use I'm putting it to; But think of a large mirror or a heavy picture. One way to make this joint even stronger is to drill 2 holes and push in dowels.