Genesis of a Dividing Head

One of the oldest problems in the world is dividing a circle into equal parts, like cutting a pie into exactly equal parts. We face this problem every time we cut a cake or pie -- how do we give everyone equal portions?  Well, I am trying to build a clock. The Isaacs clock, published long ago in Model Engineer magazine.A beginner's clock, to be sure. To do that I have to build gears. To do that I have to divide a circle into equal parts, corresponding to the number of teeth on the gear. I have a series in this blog (label "divider") on how I did it on the Taig. I built divider plates. Trouble  is, one of the gears on the Isaacs clock has 100-plus teeth. The radius required for a divider plate with that many holes in it is much too big to swing on the tiny Taig. I have learned since that there is a way around that, thanks to Tom Lipton. But at the time I hadn't watched his video.

So while I was still at Chalupy, and half my stuff was packed up, I had an idea. Every time I find a discarded printer, I take it apart. It is a treasure trove of supplies. Ground rod, plastic gears, racks, pinions, motors, name it. So I found a worm and gear of the same module (n.b. for techies, module is the reciprocal of diametral pitch, but expressed in millimeters). So I set out to build myself a dividing head. -- a gadget that will solve the cake-cutting problem very exactly.

This is a project I am making up as I go along. I regret that I seem to have lost the pictures I took at the time. I will attempt to reconstruct the process.

Above are the basic ingredients. The screwlike thing in the middle is called a worm. It is in fact a screw, rather coarse-pitch. It is on a shaft and bearing. The shaft is a piece of brass welding rod, about 3mm diameter.  Bearing is simply a square bar with a hole in the middle. Below is the gear. It happens to have 72 teeth. The gear will be pressed on to the shaft. The right end of the shaft is turned smooth. The left end is my best attempt to duplicate the Proxxon (Cecil B. de Mill) spindle, complete with collet closer. A major turning project which I did here in Anchorage. Then I can use Proxxon collets to hold the proto-gear that I wish to cut.
Now let us assemble the thing. I will cut gears  on Cecil. I have much more precise control on the speeds and movements of the mill table.

This is a real lashup which I will remedy. I hope. The clear plastic is a frame. You see the worm meshing with the gear. Now, an interesting property of worm-and-gear is thatevery time the worm turns exactly one revolution the gear advances one tooth. If we had to cut a 72-tooth gear, we would turn the shaft one turn, cut, turn one more rev, cut ... rinse and repeat. But if we wanted fewer teeth then we would have to turn more than one rev; if we want more teeth we have to turn less than one rev. We do this by using dividing plates. I have also made these things, but that will have to wait for another episode.

A commerical dividing head is quite expensive,and much bigger than my entire mill. No hope there. Proxxon builds a rotary table but very expensive. So stay tuned. This may or may not work!