yes great questions. since finding the video ive been racking my brain with the same question... how can you accurately determine the circunference of a gear when hobbing, so it doesnt leave you with an odd tooth. it has to overlap evenly through out the circumference.
so i went digging to find answers. its mind boggeling complicated!... or at least i just cant find a simple answer as you'll see here...
The Calculation of Gear Dimensions page covers the procedure for determining the sizes of gears. The size of a gear is defined by the module etc.
khkgears.net
https://www.nidec.com/en/machine-tool/knowledge/column/cutting-tool/cutting-tool-hob-02/
but but it looked so simple? for us laymen the best answers can be found by trial n error.... you just gotta do it to find out just how many teeth your hobb will cut per a set distance. then apply that to the circumference of the gear. maybe as simple as the tpi pitch of the hobb? sounds like a fun project to me.
im sure knurling works on a similar principle, except the hobb is actually cutting or shaving, rather than mashing. also it seems hobbs n taps are different although the video is using a tap.
if using small taps, you would have to be gentile on your feed rate and speeds. also working non ferrous material is much easier on the tap. after all, we arent cutting gears for a tractor's transmission.
the question of sloped teeth... in the video i did see the gear was turned over for a second cut. or perhaps a slight angle between the work and hobb can alleviate the slope? also thin gears wont have enough tooth thickness to matter.
once again, we have to put the rubber to the road instead of burning up whats left of our gray matter.
now improving traction on pullies... im sure the sacrifice is lower milage on the drive belts... thats the trade off. im not worried about the slippage, it's actually saved me in a jam a few times. I'd rather the motor keep spinning than tear up the belt.
ya gotta say, its a fun way to play with our lathes. besides, once we figure out how to make gears, there is no stopping us anymore from doing more complicated projects.
lets have some fun?