View Full Version : Ivan Law 20*PA Table

10-14-2005, 01:24 AM
On the subject of Law' G & GC, Does anyone have the corredted table for formcutters and DOC for 20* PA gears? Seems I read the table in the book contained errors. Also would like one for 14-1/2* PA, if available.

Tried the link in archives - software update error there!

TIA uute

John Stevenson
10-14-2005, 07:08 AM

The problem with cutting 14-1/2PA gear with a form tool is the undercutting on small sizes to get the correct profile.
Take a look at the outer gears in this photo:

These are 10 tooth and 14.5PA, - note the shape isn't a continious radii or involute but is undercut by the rolling action of the hob teeth in the root of the gear.
In actual fact this true shape would not be possible with a form cutter as the width of the root space is slightly larger than the gap on the pitch line.
The lower the number of teeth the worse it is.
Calculations say it starts at 32 teeth in 14.5 and 18 in 20 PA but for practical reasons we can take 25 teeth in 14.5 as being the cut off point.

Two way to attack this with form tools, One is to make a cutter up with the correct shape of multiple radii to approximate the hobbed space.
Second way is to take two cuts, one with a form tool with circles corrected to 14.5 and a single pass with a slitting type saw to open the root out.
Here is a set of tables for 14.5 to show what I mean BUT these won't work with the rest of Ivans tables.
These are for a set of tables I have done but the setup is different from Ivans.


The original article can be found at

Sir John.

10-14-2005, 12:59 PM
Thanks Sir John! A learning experience every day!

I think I'd have been wondering about that at about an assembly stage. Hmm, these gears don't seem to mesh properly. http://bbs.homeshopmachinist.net//smile.gif