What's special here is that the arbor can be inverted. Once a grind is made on one face, the arbor can be inverted on its post to grind the same face on the other pallet -- all without changing the settings of the lathe. The pallet faces are thus ground uniformly.
The inside of the pallet is ground with the outer edge of the grinding wheel. There is a little angle between the wheel and the pallet which should be kept small by adjusting the lathe carriage and cross feed. The pallet will be slightly hollow-ground, which does no harm. Run the lathe as fast as it will go.
The pallet arbor holes slip over a 1/4" post which is screwed to the lathe carriage. The fit between the post and the hole in the arbor must be quite close.
Once the correct depth between pallets and wheel is ascertained, the points on the depthing tool posts can be used to mark plates with the correct spacing.
The "Inverto" can also be used to make new pallets for an old clock. The pallets in this nice old Vienna regulator had become pitted, and "Mr. Fixit" had attempted to grind the pits out, making the pallets not recoverable.
I used the old pallets as a pattern to mark out a piece of oil-hardening carbon steel, then sawed them out with a jewelers saw, leaving plenty of extra material.
Using the clock plate, I set the points of my homemade depthing tool equal to the spacing between the escape and pallet arbor pivot holes (click on the photo for a larger image).
I also made a mount for the original Vienna escape wheel for the depthing tool - a piece of brass with a 1/4" hole in one end and another hole escape arbor diameter in the other end.
Carefully, I used the "Inverto" to grind the outside and inside of the new pallets, making frequent trips to the depthing tool to check progress. I ground the outsides of the pallets first, then the insides.
It helps to have an eye for what a deadbeat escapment looks like to do this job -- I didn't measure anything except the thickness of the original pallets, which was still readable from the remains.
Normally, the thickness of the pallet nibs is 1/2 the distance between two tooth tips, minus .015" or so for drop clearance.
Once I'd reached an approximation of the proper thickness of the pallets, I needed to grind the impulse faces to the correct angle. I estimated the angle to be 35 degrees, since that's what they usually are on these old clocks. These show as A and B in the drawing.
To make the correct angle, it's necesary to know the radius of the circle C, which is a circle centered on the pallet center, and with the angle lines of the pallet tips tangent. This makes a distance D.
A tutorial on designing deadbeat escapements can be found here.
To grind pallet angles, I made some accessories for the "Inverto". These are strips of 1/4" aluminum fitted with spikes like those on the depthing tool. They are made long to permit clamping to the bed of my 1" belt sander. The center of the spike is set out with lines to make it easier to measure distance D. There are two of them, one to put in front of the abrasive belt, the other to put in back.
The spikes are set at distance D from the front of the abrasive belt. One is used to grind the entrance pallet, the other the exit pallet.
Once again, I removed only a little material from the pallets, making frequent checks with the real escape wheel in the depthing tool, until all seems in order. If you grind off a bit much, you can always compress the pallets a bit in a heavy vice, bending them to proper locking in the depthing tool.
After the pallets are done, I polished them in the "Inverto" in the lathe, using a rubber abrasive wheel to do the polishing. The rubber wheel is a commonly-available Dremmel. It's cutting face is angled, like the cut-off wheel used to grind the pallets, to allow polishing both of the pallet arcs. After hardening the pallet tips, I polished them again to a mirror finish.
To polish the impulse faces, I set the spike on the "Inverto" at distance D from the front of the abrasive wheel to polish one impulse face, and from the back of the abrasive wheel to polish the other impulse face, as shown here.
The original pallets were mounted on their arbor using a square hole. Lacking the ability to make such in steel, I made a new arbor with a new collet for the pallets. I used the original crutch piece, which was easily mounted on the new arbor.