Gearify

[Nate]

Well said. I agree. And in the case of the gears we're discussing Im suspicious of the line of action, I dont believe there is one. More of a constant
rotation. But as I said, I'd like to hear of the experience in building a set..

I'd be curious to see how well it produces circular 'gears' too.

[ArtF]

Nate:

  You know, I like to sleep on it in things like this, because although things have a habit of looking simple,
Ive found underlying complexities in most algorithms of this sort. Your math is much better than mine, I think its
obvious from your responses to questions such as this. I appreciate that expertise being around. 

    Justin was right of course in his statement that they must slide, mine is a confusion with sliding that
causes a angular change and sliding that doesnt. I had discounted sliding that doesnt.  As you pointed
out well, sliding in the tangental direction has no effect on the rotational velocity where sliding in other
vectors necessitates it.
  Personally, I have trouble thinking of it as sliding at that point as it implies more than than
its reality. Since the contact point is touched only instantaneously and the next contact point is moving
in its own rotation coordinate system to meet the next contact point at its admittedly different speed, the result
is a roll along an involuted trajectory curve where each point meets perfectly at its own relative speed with the next
contact being the proper distance and offset away. It isnt something I think of as a slide, but it IS sliding.

  I find when I start to compete multiple coordinate frames of referance I get confused easily as to context
in those frames. Consider any single point and they meet perfectly in time and space throughout the
curve, and for this I picture no sliding. A result of knowing that temporally each point meets perfectly
with the next one in space when designing the contact curve. The curves are though, of different lengths.
Enough to hurt my head.

  So I had to look into some other assumptions to ensure I have it right. The involute is the best shape to my
mind as it keeps the line of action as pure as possible, but what about circular teeth? From a freshen-up look
this morning at my references, it appears round teeth are fine, but with the proviso the contact point is kept to the
pitch circle point or as close as possible, something which can be done by using the proper generating curve.

  In essense, the method gearify uses, is a valid one, since it is rolling a gear around another its doing a virtual hob,
Im unsure if the generation profile changes to match the contact point, but its a valid a way as any other in terms of
the generation, and if the contact point is relatively stable, then Id say a load is fine. I do think though for a round
tooth gear to work, the generating profile would change from gear pair to pair in order to match that requirement.

  In any event, thx for the explanation, I like to have my confusions in math or terminology fixed as I go.


Art


 



Thx for the update of my internal model
on how that works.



     

 
   

[Nate]

If I understand the videos correctly, then gearify may produce gears for transferring load, but it will do so by accident more than design.

A better example for non-involute gears is the imaginary gear feature in gearotic, or cycloidal gears tha were historically used in clocks.  The 'virtual hob' in gearify seems considerably less sophisticated than what would be necessary to produce one of those.

[ArtF]

Nate:

Perhaps, I find noncircluars a bitch to subtract, but its possible it works as well as any other I suppose.
  I know when I began subtraction as a build method it really had a habbit of showing flaws in my thinking,
but round teeth may be better at it. I have sent the author an invite to join us, I was pleased he contacted me,
he may be able to tell us more about the way it works. They look nice in any event.

>>A better example for non-involute gears is the imaginary gear feature in gearotic

  Actually, those were an attempt to produce a floating pressure angle involute.. Im amazed how popular they were,
I guess I may have to add them back in.. maybe Ill put them in the new wizards program.. let people script some
changes to them.

Art


Art

[John T]

Hi Art
I am not qualified to weigh in mathematically,  all I know is that my involutes don't slide if I get the center distance right. This is based on observations of my clocks running for years, If the center distance is off all bets are off.

John

[ArtF]

Hi John:

  Its really a matter of definition and context .. normally, if a wheel rolling on another slips, the speed of the two wheels must differ
for a moment, but in the case of the teeth in a gear, they can slide and not affect rotation as its a slide thats in a directional
vector that is the same as the motion..the slide allows the rotation. That having been said, its not very observable. More math
than visable reality. This slip happens while two curves roll off each other in their own motion paths...

  Ive read more treatises on tooth profile than I care to admit, but in the end, though everyone has a wizbang new profile every couple
years, they always come back to the involute it seems. Its just the best compromise you can  make for the job of gearing. I laughed the other
night in fact when I came on Gearotics Knuckle Gears. I thought I invented them, they were made years ago by someone, tested and found
to be wanting in strength. ( But their pretty.. )..

  I actually have gearify now, I've been in contact with Michael , its creator and we've swapped programs. (Developers courtesy )
Its quite well written and for those inclined to that type of gear Id heartily recommend it. He's been very cleaver in how he lets you design
the two gears.

Art

[Nate]

I am not qualified to weigh in mathematically,  all I know is that my involutes don't slide if I get the center distance right. This is based on observations of my clocks running for years, If the center distance is off all bets are off.

Here's a really nice animation:

https://www.youtube.com/watch?v=14yMFdgWM-A

It's a rack and involute pinion, but we can think of the rack as being a really big gear - so big that we don't notice the curvature.

It should be obvious that the teeth on the rack don't move up and down at all, and that the teeth on the pinion move downward (and sideways), just to the side for a moment at the bottom, and then back up (and sideways).

That means that the contact point on the rack is never moving up and down, and the contact point on the pinion almost always is.   How can that happen if they aren't sliding against each other?

[ArtF]

Very valid point, can actually be seen easier in Gearotic if you slow down the rotation on the circ gear tab, ( better resolution that way..)

Art

[jmurphycnc]

I have purchased the "gearify" software, and it is certainly fun to "play" with. Since I was a metal machinist for many years, I didn't really think this was going to produce "Technically" accurate information for practical use, but it has provided some enjoyment (toys for the granddad and the grand-kids).

My only drawback is that the dxf output from Gearify is not compatible with my Aspire software, so I have to do the "save and convert" or "Save as" in another program before it becomes importable.

For the money, I'd say it fair value.

John

[ArtF]

John:

  Yes, DXF out put can be a bear to match up with everything else, its a very nonstandard standard.. . At Gearifies price
point I think its a bargain.

Art