The arch, the upper side horizontals, and the vertical posts come together in a pair of 3-way miter joints at the top of the case. That's the short version. And from an aesthetic point of view, that's really the version that matters. As long as the joint is cleanly made, the eye will freely run along the lines of the case. But from a construction point of view, things are almost never that simple. If there are any gaps, voids, or other breaks in the surface, the eye stops there, and the mind will take note. Much like a shrieking saxophone or clarinet in an orchestra, it won't matter if the melody is miraculous. It's the shriek that you'll notice, and the reverie will be interrupted. So, to make those clean transitions, understanding what's going on is a huge help... and I didn't properly understand what was going on when I got started on this project. So I'm going to break down this deceptively simple looking joint, before we get into how it was done.
On the side of the clock, the vertical post meets the upper horizontal in a 45 degree miter. That's pretty straightforward. I'm going to refer to this as the side miter.
On the front of the clock, the vertical post meets the arch in another miter joint, that's cut at an angle that I've never bothered to measure in terms of degrees. Those miter lines point from the top corners of the case, directly to the center of the clock face. The inner radius of the arch is concentric with the dial, so the miter line runs radially through that edge. I'll refer to this as the front miter.
The curved top surface of the arch meets the upper surface of the upper horizontal members in a 45 degree miter. And I'll refer to this as the top miter. And this is where things start to get funky in the mechanics of the joint.
The plane of the cut for the side miter is at 90 degrees to the plane of the side of the clock. Or, the table saw blade is at 90 degrees to the table, when those miters are cut on those pieces. The cut for the front miter is also cut at 90 degrees to the plane of the surface. That's pretty straightforward. And in my head, that made everything seem very, very simple. That should have been a clue to me that something was awry, I guess. But because the face miter is cut at a different angle as the side miter, the edge where those two cuts intersect gets skewed to one side. So the three-way miter becomes a three way compound miter.
Each cut defines a planar surface. Geometrically speaking, two planes that intersect will define a line along that intersection. Practically speaking, that line defines the edge that's made where the two cuts come together. And for this joint to work, the edge defined by the two cuts made on the vertical post, the edge defined by the two cuts on the horizontal member, and the edge that's defined by the two cuts on each end of the arch... those three edges must come together cleanly along their length, with all of the mating faces coming together fully.
The test joint actually came together cleanly, but if you zoom in on the picture, and see the different surfaces interacting, you'll start to get an idea of just how many things can go wrong in the joint. Oh, and having one of these come together is hard enough. To cut the arch properly, there are two of these joints to consider, one on each end. Which brings us back to the top miter.
To cut that compound miter, the 45 you see on the surface is defined in relation to the top edge of the horizontal, and the back edge of the arch. The angle of the blade during the cut, which is what makes this a compound miter, is defined in reference to the surface of the parts that will lie flat on the saw table.
But the top is curved. There is no reference surface.
Obviously, to be continued...