The Home Machinist!

Opps! You're right. Probably only works with HF drills.

If one is lucky, otherwise there is not enough Carbon in recycled soup can to harden.
Bashing HF is a popular sport but actually their tool quality has improved, still cutting tools are iffy.

Same here. I save any hard tool steel. Tap and even dies, I made a form tool out of a broken scissor blade. Too thin to be used flat but supported with a blank worked fine.

you can fix that with a torch and bucket of water.

Not HSS. Hardening HSS is a not a process available at the typical Home Shop Guy.
I make cutting tool from broken HSS bit but the only useful part is the web which basically limit the design to small grooving tool.

Well, I saw it on the internet so it must be true. Yea.

I was watching a guy on Utube making late tools from the shank of HSS broken drill bits. I pointed out the the shank is not hardened. He responded that in his case it is because he uses HS Conbalt. That makes no sense since an alloy element added to improve the business end of a drill has no bearing...

The OP was not about drawing, printing, machining an Hyperbola. The OP was: Given the position of the stick on the twirler rotating disk, what is the equation of the Hyperbola to cut the slit so that the stick pass through? Reference to a contraption like: https://www.youtube.com/watch?v=cfrQSzDfFoI...

All good points but no CNC here, only dials. I was a bit lazy but being in vacation near Buffalo (I know, who would vacation in Buffalo) between the never ending rain and the cows in the pasture I got down and worked out the geometry. The slits are definitively an Hyperbole an not a Parabola, that w...

I am aware of the examples.
I am looking for dimensioned plans OR an analytical way to relate the position and inclination of the revolving "stick" to the projection on the plane-on-axis where the hyperbolic slits are cut.

I have the same miniature bevel gears in a PM Shaper Model. Is fundamental that the gear mesh properly and the virtual cones meet at the same point where the axis meet. Washer and/or collars to position the shafts.

I want to build one of these.
https://www.youtube.com/watch?v=cfrQSzDfFoI

Anybody has plans or formulas to cut the Hyperbola given the rod mounting attitude and location?

A rectangular cotter pin with the aspect ratio shown has great strength against axial pull out of the clevis pin, yet it may be built as an hairpin with a head to keep if from falling through and made springy to stay put while easy to be compressed by hand. Flexible in one direction and strong on th...

When clamping a piece on the end of the vice, place the jack on the other side to eliminate the twisting load.