"Projects" at georgesbasement.com 

Upgrading an Old (U.S. Pat. No. 432,621) Cincinnati Milling Machine Co. Indexing Head
Gease off
Gresas off
   Once I got all the grime off of this old indexing head, I realized that it had the potential to do differential indexing, as the shaft (driven by the mitre gears off the worm-driving shaft to which the crank is attached) is parallel to the spindle when the spindle is aligned horizontal, i.e., parallel to the base of the indexing head.
   In the image above the tail of the spindle is threaded to affix the indexing drum described in the device patent (U.S. Patent No. 432,621) and direct indexing is done by locating the drum with the index pin at the bottom of this image. I found no damage other than dings and scratches that couldn't be fixed with a triangular file. I adjusted the worm easily.
Holz patent 432,621
Worm gear adjustment
Drum cross section
   The text of U.S. Patent No. 432,621 reveals that the inventor Frederick Holz did not contemplate differential indexing - just spirals and plain indexing, either with the drum (image at far right) or with the crank and disk of circles (above).
   Figure 5 from the Holz patent shows how the worm gear is adjusted for backlash - easily accomplished when the head is rotated in its trunnions so that the spindle nose faces straight down - and how the spindle is clamped by the knob at K'.
   The drum U is missing from my example of the indexing head, but you will see that I have made a rearward-facing extension of the spindle which will accommodate a new drum made from an old flat-belt pulley.  What are the drum's specific hole counts ?
  Spindle extension
The spindle extension shown in place at left is entirely one piece, with a 1.375-18 thread at the large end to fit the rear of the spindle and a 1/2-13 thread at the small end for the clamping nut that affixes the South Bend size 18 diametrical pitch gears (0.563 inch bores) that I'm currently making.  There's room for two thicknesses of gears (i.e., 0.375 times two plus a spacer) because the spindle gear is often called upon to drive a compound gear to effect the necessary ratios for differential indexing.  The T.I.R. of this extension is 0.001 inch, whch I achieved by doing most of the boring & threading between centers or with a steady rest and center.  The central thread is 1.500-8 to fit South Bend headstock accessories and to affix the new drum, which is moved back close to the change gears to maximize the strength of the spindle extension.  I cleaned up the spindle's threads with a three cornered file until the extension would thread onto the spindle by hand.  The ID also fits closely (0.001 inch) to the OD of the unthreaded portion of the spindle.

   The nut seen on the worm shaft at lower left was frozen to its threads because it had been improperly tempered (i.e., not at all) and had cracked.  Luckily, I found a replacement that is sound and nicely made.

   There's no place on the housing for the worm shaft to which a banjo can be attached to support the change gears, so I'll be making a separate frame that attaches to the machine table to which the brackets for the change gears will be clamped.  I did find a thread on Practical Machinist that involved the sale of a dividing head like this one that was outfitted for differential indexing with a bracked held by the T-slot for the direct indexing pin bracket and a bearing on the spindle extension.

  My gear-making task is made a little harder because the diameter of the worm gear
shaft is 1.250 inch.  That precludes affixing 18DP gears with fewer than 30 teeth.  I've cut most of the blanks for the gears from steel bar stock (up to three inches) or Class 40 cast iron in continuously cast bars four inches and six inches in diameter.  The six inch piece was six inches long, and the four inch piece, four inches long.  I've converted all of one and all but 1/4 inch of the other piece entirely to gear blanks or index-plate blanks (for two other projects) plus a huge pile of chips.

Making indexing disks Gear blanks
The OD turning and facing operation at upper left was being done on the second or third blank. Note that the 5-1/8 inch diameter cast iron round barely clears the compound of this nine inch lathe.  A six inch OD piece would have to be worked on with a boring bar and overhung from the chuck, making work on pieces this large not such a good idea.

   The image at upper right was made after I had made a large number of blanks.  I found that I could cut the blank nearly entirely free with this cut-off blade by stopping the lathe every so often and extending the blade farther from its holder.  Then I could simply break the last quarter inch by prying gently with a screwdriver.

   Yes, there was considerable chattering until I learned to adjust the blade slightly below center; if it was at or above center it screeched loudly.  With the blade below center I could feed it into the cut as long as that required some effort; once it started feeding in too easily, I prudently stopped the cut so as not to let the workpiece climb on top of the blade.

   I sharpened the cutoff blade before every cut.
   The Cincinnati dividing head has a limited number of hole circles; specifically, it is missing the 20-hole and 16-hole circles, so I have modified the classical Brown & Sharpe Plain & Differential Indexing tables (from the 1916 edition of Milling and Milling Machines published by Brown & Sharpe Mfg. Co. in Providence, RI) to accommodate that deficiency and also to omit use of 24 and 28 tooth gears on the worm shaft.  In the tables below, the modifications are in blue typeface.  In Mozilla-type browsers you can right click on an image to see it full size. Don't try these at home without checking the amount of revolution for one division with a dial indicator or vernier protractor and a level; there are no guarantees that the blue numbers are correct !  I did find one typo in the B&S table: for 83 divisions, which appears to ask for 10 holes out of 20 on a 26-hole circle; that's become 15 holes out of 30 on a 30-hole circle below.
Table 1
Table 2
Table 3 Table 4
Table 5 Table 6
Table 7 Table 8
Table 9 Sample Calculations. 
Brown & Sharpe's engineers spent a lot more time than I have to work out these ratios so as to minimize the need for many gears.  I have not been able to reproduce their logic, but the following examples seem to work OK, once one gets the rotations correct. 

128 divisions:
128/3 = 42-2/3 ... 2-2/3 = 8/3, so spindle to worm ratio is to be 8/3 or 64/24 teeth, using available gears.  24 tooth gear is N.A., so use 64/48 times 60/30 compound gears. Add idler(s) so index plate turns 42-2/3 times while spindle is turning one revolution.  To get 128 divisions, turn crank 13 of 39 holes (one-third revolution) for each division. Three times 42-2/3 = 128.
211 divisions:
211/5 = 42-1/5 ... 2-1/5 = 11/5, so spindle to worm ratio is to be 11/5 or 55/25. 25 tooth gear is N.A., so use 55/50 times 8/5 = 55/40 times 48/30 compound gears.  Add idler(s) so index plate turns 42-1/5 times while spindle is making one revolution. To get 211 divisions, turn crank 6 of 30 holes (one-fifth revolution) for each division. Five times 42-1/5 = 211.
269 divisions:
269/7 = 38-3/7 = 40 - 1-4/7 ... so spindle to worm ratio is to be 11/7 or 33/21 = 33/42 times 60/30.  Add idler(s) so index plate turns 40 times less 1-4/7 revolution while spindle is making one revolution.  To get 269 divisions, turn crank 4 of 28 holes (one-seventh revolution) for each division.  Seven times 38-3/7 = 269.