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Nate
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« Reply #45 on: September 25, 2015, 05:12:03 PM »

...
In the above diagram, the circular gear has a line of action who's position (I'm talking about the entire line segment's position) remains constant relative to (let's call it) the observer. But the non-circular gear has a line of action that is at a different horizonta l location. So, either the horizonta l position (relative to the observer) of the line of action would need to jump to new horizonta l position after each tooth engagemen t, OR, the location of the line of action is allowed to vary continuou sly over a single tooth (in which case the "dots", which are interpola ting across a moving line, would actually follow a continuou s curve).
...

It's the latter - the pitch radius can vary continuou sly over a single tooth.
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ArtF
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« Reply #46 on: September 26, 2015, 09:02:04 AM »

>>the location of the line of action is allowed to vary continuou sly over a single tooth (i

I think thats true since the tangents to the base circle vary from point to point the line of action is variable over time and over the run of each tooth.

   I tried an appraoch I recall where you calculate the base circle, then unwind the involutes point by point from that base circle..

(. problem had something to do with actually computing a base circle in convex areas.. requires looking to the inside curvature, not the outside.. Negative curvature s caused me trouble as involutio n switches polarity so to speak.... Hard to explain till youve coded it I think, or its just my weaker math skills, ). Perhaps, Michael your comment on the sudden shift is related to that thought, there is a point at which the involute shifts direction as K changes polarity. That could by considere d a sudden shift...c onceptual ly..thoug h its really a reversal with decelerat ion and accelerat ion into the new direction of curvature .


Art
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Nate
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« Reply #47 on: September 26, 2015, 09:20:41 AM »

... problem had something to do with actually computing a base circle in convex areas...

When you have a negative curvature, then the center of the osculatin g circle is on the other side of the roll line, and when the curvature is zero, the circle is degenerat e.

I have to say, my eyes crossed a little when I read "... shrink the ellipse by the base circle amount ..." earlier.

As far as I can tell, base circles are great when you want to generate the gears on paper using physical tools like string and pencils, but really only confusing when we have the analytic power of modern computers available .

P.S.  Is the "WiredMind s eMetrics" in the preview supposed to be there?
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Nate
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« Reply #48 on: September 26, 2015, 09:22:06 AM »

... problem had something to do with actually computing a base circle in convex areas...

When you have a negative curvature, then the center of the osculatin g circle is on the other side of the roll line, and when the curvature is zero, the circle is degenerat e.

I have to say, my eyes crossed a little when I read "... shrink the ellipse by the base circle amount ..." earlier.

As far as I can tell, base circles are great when you want to generate the gears on paper using physical tools like string and pencils, but really only confusing when we have the analytic power of modern computers available .  Though if they work, by all means, keep using them.

P.S.  Is the "WiredMind s eMetrics" in the preview supposed to be there?
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ArtF
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« Reply #49 on: September 26, 2015, 12:21:35 PM »

>>As far as I can tell, base circles are great when you want to generate the gears on paper using physical tools like string

  lol, your probably right, but I tend to figure these things out with trigonome tric analysis, my backgroun d is not such that I can
create the equations necessary to bypass the informati on things like the base circle give me. One of the papers Ive used in the
past for involutio n theory on a noncircul ar gear was based on doing exactly that, they included a formula for the base curve of the ellipse
as it relates to the tangents of the ellipse,( it really isnt a shrunken ellipse, the profile actually crosses over with curvature)
 from there they suggested an involutio n based on  point by point changes in that base curve.
   I did attempt their suggested procedure , but found it was really no more efficient that what I was doing codewise, so moved on to
virtual hobbing..

Art
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Nate
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« Reply #50 on: September 30, 2015, 09:18:54 AM »

Quote
... my backgroun d is not such that I can create the equations necessary to bypass the informati on things like the base circle give me. ...

I've been musing on this, and am unsatisfi ed with the explanati on that I gave earlier:  it's not practical, doesn't address things like planetary gears and racks, and doesn't provide insight into how I'm thinking about things.

What language(s) are you guys coding in?
« Last Edit: September 30, 2015, 09:33:55 AM by Nate » Logged
ArtF
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« Reply #51 on: September 30, 2015, 10:14:59 AM »

Nate:

>>What language(s) are you guys coding in?

  C++ here.
 
    I know what you mean, language is a problem. Something like a base circle not being considere d isnt really
accurate to me if we consider an oscculati ng circle.. which is really an analogue for the actual base circle. Circle though becomes
poor terminolo gy as its neither a circle nor neccesari ly inside the ellipse.  I guess I consider the term  "the tangental 
series of points defined by the objects pressure angle calculati ons" ... but its easier for me to consider that a base circle. Smiley
  Either  way you try to describe a solution, I suspect its more an algorithm ic discussio n as Im sure its solvable, Im just not willing
to do 30,000 lines of code to do so. When I get far enough away from an elegant solution, I wait till I have one. Hobbing
works well as it takes the trochoida ls into account in the more extreme noncircul ars.
  That having been said, I welcome the discussio n on a better and more elegant method, I do like it when the numbers line up.,
and your ideas sound like they have a lot going for them..

Art

 
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Nate
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« Reply #52 on: September 30, 2015, 05:26:14 PM »

...

If measured from (p1-p2) I feel that there would be severe disortion s where t1-t2 differs significa ntly. But if from t1-t2, the gears may not "push" on eachother properly and the entire benefit of involute teeth is compromis ed.

Thoughts?

It looks like I misrememb ered, and you want to use the tangent line for gears that are that eccentric .

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ArtF
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« Reply #53 on: September 30, 2015, 08:46:13 PM »

>>It looks like I misrememb ered, and you want to use the tangent line for gears that are that eccentric .

   So is that a drawing of using tangent lines of the shapes themselve s? Or pressure angle calculate d
tangent points, or osculated circle tangents?


 ( Ill be away starting tomorrow for 12 days. Ill catch up then. Smiley )

Art
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Mooselake
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« Reply #54 on: September 30, 2015, 10:19:48 PM »

Enjoy your vacation!  Try not to think about gears Smiley

Kirk
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Nate
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« Reply #55 on: September 30, 2015, 11:56:22 PM »

>>It looks like I misrememb ered, and you want to use the tangent line for gears that are that eccentric .

   So is that a drawing of using tangent lines of the shapes themselve s? Or pressure angle calculate d
tangent points, or osculated circle tangents?

...


The pressure line is off the tangent line by the pressure angle.  I.e. rotating the analogue of the t1-t2 line by the pressure angle.

Enjoy the vacation.
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ArtF
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« Reply #56 on: October 01, 2015, 06:36:11 AM »

Nate:

 >>The pressure line is off the tangent line by the pressure angle.  I.e. rotating the analogue of the t1-t2 line by the pressure angle.

   Yes, I agree. What Ive been referring to as the base circles, are those tangent points set at the same distance from pitch point ( cos of the elliptica l radius) as the base circle normally is, so  I still refer to them as a base circle points as they are an analog of the same thing in a circular gear. I think for the most point were speaking the same thing, in different languages . Originall y, I used to use that (cos()*R) at pressure angle to determine each of the  base points for any point in the rotation, then calculate the involutio n from that point. Now all that was ,to my mind ,necessary to pick a start point for the involutio n to occur, but
as you stated it, calculati ng a running contact point up that line sounds better and easier, with no need to
figure the involutio n angles involved. . maybe..

  >>Enjoy your vacation!  Try not to think about gears

  I will and Ill try. But Ill fail. lol  Thx
Art
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Gearify
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« Reply #57 on: October 30, 2018, 10:11:16 AM »

Hello!

Some of you may be intereste d to know that Gearify is developin g a new tool for the generatio n of involute teeth on arbitrary pitch curves.

Teaser video can be seen here:
https://youtu.be/8aOFbEwis1w

I made an in depth mathemati cal analysis to understan d how the constrain ts and degrees of freedom change at each point along the curve and made some intriguin g discoveri es.

Feel free to leave questions or feedback. The tool is not released to the public yet, but if anyone has a significa nt and immediate need for such a tool, we can discuss.

-Gearify
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ArtF
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« Reply #58 on: October 30, 2018, 02:23:47 PM »

Looks good. Looks very similar as to how Gearotic does it, a digital subtracti on where the involute evolves from the instantan eous rate of change during its construct ion? I find it works well until pressure angle drops too much , then the gears fall apart in real life running while they simulate fine. Backlash tends to be an issue
depending on contructi on and elliptial coefficie nt. They look good though, generatio n seems smooth.

Art
 
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Mooselake
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« Reply #59 on: October 31, 2018, 01:28:26 PM »

Glad to see new developme nt with Gearify!

Kirk
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