Help wanted with sanity check for a 40PA hob cutting tool

[CanBeDone]

Instead of answering your implied questions, I will provide you with a link. From that link I have taken this photo

which shows a simple way to cut gears using a vertical mill. If you follow the link provided by AI8236, you'll end up on a web site that very much has written down what I think on how to design a gear cutter - VERY different from your ideas. If you add to this that you can buy finished gear hobs for under 50 US$ from e.g. aliexpress.com, that is the way I would tackle gear cutting.

[DIYSwede]

Thanks again for your input and links, CanBeDone.

Realizing that I might be perceived as being polemic and/ or "resistant to counseling",
this is neither my intention, as I try to consider facts and opinions of others on the fly,
and relate these to the capabilities, conditions and limitations under which I strive,
nor is it an expression of any self-pity regarding my lack of a "proper workshop" :

I do agree with you that a "rack-cutting mill" as per Al8236, Helichron and several others is a simpler way than my suggested prototype.
As I neither possess a mill nor a dividing head, and absolutely not the patience/ time needed for cutting a gear through stepped indexing:
To get a decent tooth profile, you'll need at least 4 cuts/ tooth - that would mean >216 indexed steps/ cuts for the pictured 54t gear above.
Link: Gear cutting with a rack form multi-tooth cutter

The only advantage I see of a mill tool of this type compared to standard gear cutters, is that you don't need the 8 cutter set/ module or DP.
OTOH, a cutter would only need 1 index and cut/ tooth whereas the rack mill needs several to get a decent tooth profile.
Of my self-imposed design criterias, the "operative" wouldn't thus be met (I forgot "fast" as also one of my criterias)

My quick & dirty prototype (absolutely NOT my invention) having a single helix hob with at least 6 cutting edges/ turn and a "lead screw",
will achieve both a good enough tooth profile for ANY (20+) tooth gear count gear of the given module/ PA,
as well as a real fast synchronized indexing of the blank - getting a "plastique" gear duplicated to brass, steel or CI within minutes.

Another happenstance consequence in my prototype's design, is that by having multiple module/ DP & PA pairs of DIYed hobs/ lead screws,
I would be able to make a (say) 57t 1M 20PA gear from any pitch/ PA 57t gear, as long as the diametres are within +/- 25 %,
by merely changing the lead screw/ gear and "stooping" the blank holder for difference in gear radii.

Lastly - buying hobs would "violate" my DIY CHEAPNESS design criterium, and also not achieving my silent quest for "hard fun",
as in cutting, relieving*, hardening, annealing and grinding hobs in the "walk-in closet workshop".

Now I'll get started grinding the 0.5M 40 deg cutting tool with a .4 mm tip width.

Cheers

Johan

*DIY Gear Cutter: The Eureka Tool