Non-Circular Gear Theory

[JustinO]

"Noncircular Gears, Design and Generation" Faydor L. Litvin.

This subject is discussed.

[Mooselake]

Nate:

>>If I understand correctly, the 'gear ratio' should be the first derivative of the formula that is entered.  That's useful for creating a particular motion, but not so great for making a particular gear shape.  (Of course, you'd have to be a little loony to want a particula r gear shape...)

  Correct. The formula uses t as a descriptor for angle, it is specifically asking for a t2 ( angle of the second gear) in relation to t1 ( angle of the first gear.) I designed it for many that wrote me asking for a formulaic motion designer, as you said youd have to be looney to want to use a formula for shape..but then Im frequently descibed as looney... so Ill give some thought as to allowing that as an option on the designer. Im never against the artistic merits of any shape.

Art

I must have forgotten that, along with the contents of my calc and diffeq classes.  Strange that it comes close to what I was expecting.  Also explains why using sin(t) instead of cos(t) did a lot more than a shift from x to y.  Maybe it's time to hit one of those online intro to calc classes and see if some of it'll come back; didn't have those the first time around.

t+cos(t)/4 gives a slightly out of round circle.

Kirk

[Nate]

t+cos(t)/4 gives a slightly out of round circle.

Yeah, I don't have the 'right' formula handy.  You could try tweaking the coefficient on the cosine - t+cos(t)/1.414 should be a bit more out of round.

Edit:
Based on the numbers I generated, you could try 1.1t+sin(t)

Re-Edit:
That should be t+0.8 sin(t)

[ArtF]

>>"Noncircul ar Gears, Design and Generatio n" Faydor L. Litvin.

Litvin is the master. Ive read most of what he's written, and lately Ive found things I must go back and revisit
as my math skills have improved over the last couple years.

Art

[Nate]

  On gears such as you have pictured, the issue often isnt the pressure angle. Its the toothing, depending on the teeth they can be hard to place
in concavities.

It doesn't seem *that* bad, though I haven't tested them.

[ArtF]

doesnt look too bad..

Art

[Nate]

...
Correct. The formula uses t as a descriptor for angle, it is specifically asking for a t2 ( angle of the second gear) in relation to t1 ( angle of the first gear.) I designed it for many that wrote me asking for a formulaic motion designer, as you said youd have to be looney to want to use a formula for shape..but then Im frequently descibed as looney... so Ill give some thought as to allowing that as an option on the designer. Im never against the artistic merits of any shape.
...

As long as you're volunteering to do silly things... how do you feel about non-circular bevel gears?

[ArtF]

Strickly speaking, wouldnt that be impossible? Well, I mean I guess one could have a movable shaft version.. but in trying to imagine some
other configuration in my head makes it hurt.. :) .. Though I guess one could design one something liek a crown gear which has varying height as opposed to haveing the shaft move.... Ill have to think about that one..

Art

[Nate]

Strickly speaking, wouldnt that be impossible? Well, I mean I guess one could have a movable shaft version.. but in trying to imagine some
other configuration in my head makes it hurt.. :) .

It seems like it should work the same way that planar non-circular gears do, just spherical geometry instead.  I'll see about modeling and making a pair...

[JustinO]

I shaved an almost correct pair of spherical NCGs, but I need another axis. I've mostly built a machine that should make a theoretically correct pair. The more axes I add, the simpler the math gets. I need another parallel port and sixth Gecko 203v.

Yes, I'm completely mad. Mwahahahahah!

[Nate]

I shaved an almost correct pair of spherical NCGs, but I need another axis. I've mostly built a machine that should make a theoretically correct pair. The more axes I add, the simpler the math gets. I need another parallel port and sixth Gecko 203v.

Yes, I'm completely mad. Mwahahahahah!

I don't understand why you'd want or need more than a 5th axis.

[Nate]

Strickly speaking, wouldnt that be impossible?...

I think I've modeled a matching pair of gear profiles.  Can anyone suggest good tools for closing up the STL to print them?

[ArtF]

hard to imagine how that rotates without shaft motion.. I dont doubt it does of course, its just hard to imagine. :)


Your good..

Art

[JustinO]

Nate, the additional axes make the math easier.

[Nate]

I printed up a pair, the meshing is not great, though I'll blame that on the print quality for now.  ... I'll probably print some more and see if I can make a working bevel gear turntable.