Drop Leaf Rule Joint
While at first glance the rule joint seems simple, the realities of this joint can be frustratingly troublesome. A first attempt will often result in a joint that scrapes and binds or leaves unsightly gaps. To get it right the first time requires both an understanding and application of the geometry at work.
These days the majority of us will cut the rule joint profiles with a router. Though this tool can quickly produce a very accurate pair of matching cuts, it can just as easily cut a good looking but unworkable joint.
Because different hinges will require different settings for your router, hinge selection must be your starting point. A rule joint hinge is specially manufactured with an extra wide leaf to span the joint. Because it is screwed into the underside of the table with the barrel facing up it is countersunk on the reverse side.
Start by opening the hinge and laying it barrel upward on a flat surface. Accurately measure up from this surface to the center of the hinge pin. In the case of our standard drop leaf hinges this measurement will be 1/8" (Alternatively, and assuming the hinge is a traditional flat back style you can simply measure the hinge barrel and divide by two). When this hinge is mortised into the underside of the tabletop the center of rotation of the table leaf will be 1/8" up from the bottom.
Most tabletops are built of 3/4" thick material and so it seems reasonable to select a 1/2" radius cutter for the joint. Many woodworkers cutting a rule joint for the first time will fail to take into account the center of rotation described above and will assume a 1/2" radius cutter will leave a 1/4" fillet in 3/4" stock. If a 1/2" radius cutter is set correctly, with the center of its described circle raised 1/8" above the underside of the table, the fillet will actually be only 1/8" not 1/4". An 1/8" fillet is a workable minimum because, while the fillet is cut into the tabletop, the table leaf must match its profile with perhaps 1/32" clearance. With a full 3/4" material thickness, that will leave an edge of 3/32" which should be regarded as the absolute minimum. If the tabletop is thinner due to planing or sanding, then a 1/2" radius cutter will be too large and must be abandoned in favor of a 7/16" or smaller pair of bits.
After having established the center of rotation as defined by the hinge choice and having selected the cutter, you can run the profile on the table top. If you are using a 1/2" radius cutter you will need to set the base of your router to cut a fillet of a thickness that is the result of the following formula:
Tabletop thickness (3/4") minus 1/2 hinge barrel diameter (1/8") minus cutter radius (1/2")
With this profile cut you can run the mating profile in the table leaf. Ideally you would select a cutter with a 1/32 larger radius to provide a little clearance at the joint. Such cutters are not generally available, so in order to create the needed clearance, you will separate the leaves by this much when installing the hinges.
The hinges can now be mortised. The first cut will be in the table top and will accommodate the hinge barrel. This is best cut with a Ό straight cutter. The center of this cut should be a 1/64 outboard of a line drawn down from the vertical cut left by your radius cutter. With the table top upside down and with its leaf nesting in place but separated by 1/32, lay the hinge barrel in its mortise and with a sharp knife scribe its outline. Finally route a mortise to set the hinge flush with the table underside and screw into place. Make sure the table leaf remains firmly in place during this operation.