I've been reading Ivan Law's book on making gear cutters and he described
the design and build of a "button cutter" to generate an approimation of the
Mr. Law sets out two tables of design information for the cutters, one
20deg pressure angle and the other is at 30deg pressure angle. The design
data is normalised at one diametrical pitch.
The puzzle I have is that the two buttons are of diameter "D" and the
distance between the button centres is "C".
The thing I'm struggling with is that in both tables "C" is less than "D".
How can this be?
Too be honest it's a bit of an armchair question as I've had a kind offer
from one of the guys on the group to cut the two gears I'm after, but can't
abide leaving things I don't understand to one side!
C is less than D to make cutters to cut gears with the smaller number
of teeth. In those cases, you have to grind flats on the buttons in
order to get the required distance apart. It's all to do with the
geometry of involute gear teeth.
I have a pencilled note in my copy saying that there is an error in the
table/tables on P114/5 and that there was an amendment published in
Model Engineer, P744 15th June 1990.
I remember copying it and placing it carefully in the book - but damned
if I can find it now. Maybe some kind soul has that issue handy?
Search the newsgroup for "Ivan Laws" and you will find a couple of
threads on this topic and one contains a link to a spreadsheet written
by Duncan Munroe. I ended up concluding that there is an error in the
tables in my 2006 copy of this book, but as I was after 14.5 degree PA
then I had to resort to my own calculations anyway. It is a shame that
Ivan Law didn't spell out how he calculated the numbers in his tables
so we could check his workings - but on the other hand it is important
to realise that circular cutters are only an approximation to the
involute, and even pre-made cutters cover a range of gears. So there
is a fair bit of tolerance.
Steve (yes, another Steve)
I have a spreadsheet that will calculate these values. You can see it here:
It calculates the button diameter, pitch and infeed for the form tool
described by Ivan Law in his book "Gears and Gear Cutting". To obtain
actual sizes then either divide by the DP of the actual gear to get
sizes in inches or multiply by the module to get sizes in millimeters.
The table in the book is acknowledged as being in error and other tables
exist on the 'net. One of these can be found here:
(written by John Stevenson)
An article in Engineering in Miniature (Oct 1998) by D A G Brown
describes the process and gives a set of formulae for calculating the
relevant dimensions. I have used those calculations in this spreadsheet.
The calculations are a bit scruffy but accurate in as much as they
replicate the results of DAG Brown. Where those results differ from
other published tables there are a couple of reasons. One is rounding
errors. Another is that the tables often give dimensions for a cutter
intended to cover a range of gears. The compiler of the table may have
chosen any particular number of teeth for that cutter in the range quoted.
In general it seems that close enough will do. For example, take the No4
cutter (26-34 teeth). For this, the range of button sizes is 8.89 to
11.63. Any button size you pick will be an approximation for the other
A related discussion I came across had the following suggestion from
Jerry Kieffer: He makes single point form tool by using an end-mill to
cut the profile out of a suitable blank. He says that for any given
gear, there will probably be a standard size end mill of a diameter
close enough for the task in hand. So for example, to make a 48 tooth,
0.5module gear, the button diameter would be 16.42 * 0.5 = 8.21mm. An
8mm end mill would be quite close enough using Jerry's method.
Please note that I have never had to make my own cutters but expect to
one day which is why have taken the trouble to keep track of these bits
So you did! I remember now. I have a similar, but less thorough, page here:
But didn't you, or soeone, do a further piece about using CNC on the
cutter position to get a much better generated shape?
As an aside, seeing your page prompts me to haul out my Peatol lathe and
make it into a tool sharpener. It was going to go on Ebay but I don't
think they fetch much.
That would be a straightforward thing to do - I made a passing comment
in the article that it would be simple enough to do if you had a CNC
mill to hand, but haven't actually don it (yet).
The great thing about that technique is the simplicity of the cutters
- it doesn't get much simpler to make than a rack form cutter.
Yep - good plan.