Some reference work reveals that the number of holes listed above as Plate A, B, C are standard Brown and Sharp, known for nearly a hundred years. Page 1873 of the Machinery's Handbook, Edition 25 details their usage. (There is also another standard called the Cincinnati.) The machine from PM looks like a distant cousin of BS.
Sure enough it has been well known that not all divisions are possible with 'Simple' indexing. So, my hack did not produce knowledge, except only to me. Simple indexing (SI) is turning the hole plates so that a known number of holes in one ring of holes pass a reference point. It produces exact divisions (depending on the accuracy of the hole location, of course). The chart on pages 1876 through 1878 of the above reference lists the 'exact' divisions that are possible with the holes in plates A, B, and C.
These dividing heads can be used in 'Compound Indexing', (CI). CI is where two or more rings of holes are used to turn the work. The table mentioned above lists all divisions from 2 through 250. Some CI produce exact divisions. But many produce approximate divisions, where the error is 0.001 inch ( 1 mil ) in a circle of many inches, typically 10 or more inches.
The handbook gives a specific example, described in words, for division by 127. The error is 1 mil in a 17.5 inch diameter circle. The hole-rings to be used are the 39 and 47, (they happen to be on Plate C). The the movement of the work piece is by 2/39 plus 42/47, three index points apart, (42 holes on the 47 ring plus 2 holes on the 39 ring); but this skips two index points; and it takes three revolutions of the work piece to catch all 127 index points.
It's hard for me to believe that hole locations are within 1 mil accuracy. Therefore, the arithmetic approximations given by the CI method is good enough: the limiting factor is the hole location and the precision of the worm gear.
I think I continue to keep the dividing head in my shopping basket.
Sure enough it has been well known that not all divisions are possible with 'Simple' indexing. So, my hack did not produce knowledge, except only to me. Simple indexing (SI) is turning the hole plates so that a known number of holes in one ring of holes pass a reference point. It produces exact divisions (depending on the accuracy of the hole location, of course). The chart on pages 1876 through 1878 of the above reference lists the 'exact' divisions that are possible with the holes in plates A, B, and C.
These dividing heads can be used in 'Compound Indexing', (CI). CI is where two or more rings of holes are used to turn the work. The table mentioned above lists all divisions from 2 through 250. Some CI produce exact divisions. But many produce approximate divisions, where the error is 0.001 inch ( 1 mil ) in a circle of many inches, typically 10 or more inches.
The handbook gives a specific example, described in words, for division by 127. The error is 1 mil in a 17.5 inch diameter circle. The hole-rings to be used are the 39 and 47, (they happen to be on Plate C). The the movement of the work piece is by 2/39 plus 42/47, three index points apart, (42 holes on the 47 ring plus 2 holes on the 39 ring); but this skips two index points; and it takes three revolutions of the work piece to catch all 127 index points.
It's hard for me to believe that hole locations are within 1 mil accuracy. Therefore, the arithmetic approximations given by the CI method is good enough: the limiting factor is the hole location and the precision of the worm gear.
I think I continue to keep the dividing head in my shopping basket.