Gearify

[Nate]

...
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 horizontal location. So, either the horizontal position (relative to the observer) of the line of action would need to jump to new horizontal position after each tooth engagement, OR, the location of the line of action is allowed to vary continuously over a single tooth (in which case the "dots", which are interpolating across a moving line, would actually follow a continuous curve).
...

It's the latter - the pitch radius can vary continuously over a single tooth.

[ArtF]

>>the location of the line of action is allowed to vary continuously 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 curvatures caused me trouble as involution 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 considered a sudden shift...conceptually..though its really a reversal with deceleration and acceleration into the new direction of curvature.


Art

[Nate]

... 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 osculating circle is on the other side of the roll line, and when the curvature is zero, the circle is degenerate.

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 "WiredMinds eMetrics" in the preview supposed to be there?

[Nate]

... 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 osculating circle is on the other side of the roll line, and when the curvature is zero, the circle is degenerate.

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 "WiredMinds eMetrics" in the preview supposed to be there?

[ArtF]

>>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 trigonometric analysis, my background is not such that I can
create the equations necessary to bypass the information things like the base circle give me. One of the papers Ive used in the
past for involution theory on a noncircular 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 involution 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

[Nate]

... my background is not such that I can create the equations necessary to bypass the information things like the base circle give me. ...

I've been musing on this, and am unsatisfied with the explanation 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?

[ArtF]

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 considered isnt really
accurate to me if we consider an oscculating circle.. which is really an analogue for the actual base circle. Circle though becomes
poor terminology as its neither a circle nor neccesarily inside the ellipse.  I guess I consider the term  "the tangental 
series of points defined by the objects pressure angle calculations" ... but its easier for me to consider that a base circle.
  Either  way you try to describe a solution, I suspect its more an algorithmic discussion 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 trochoidals into account in the more extreme noncirculars.
  That having been said, I welcome the discussion 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

[Nate]

...

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

Thoughts?

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

[ArtF]

>>It looks like I misremembered, 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 themselves? Or pressure angle calculated
tangent points, or osculated circle tangents?


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

Art

[Mooselake]

Enjoy your vacation!  Try not to think about gears

Kirk