## Gearify

### Re: Gearify

I think I'm not communicating what I am trying to say properly. I do understand composition of continuous functions is continuous. I think we're talking about two different things but I'm not sure where our disconnect is yet.

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).

Do what I' m saying make more sense now?

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).

Do what I' m saying make more sense now?

### Re: Gearify

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

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).

...

### Re: Gearify

>>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

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

### Re: Gearify

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

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?

### Re: Gearify

Nate wrote: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.ArtF wrote:... problem had something to do with actually computing a base circle in convex areas...

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?

### Re: Gearify

>>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

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

### Re: Gearify

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

What language(s) are you guys coding in?

Last edited by Nate on Wed Sep 30, 2015 3:33 am, edited 1 time in total.

### Re: Gearify

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

>>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

### Re: Gearify

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

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?

### Re: Gearify

>>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

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

### Re: Gearify

Enjoy your vacation! Try not to think about gears :)

Kirk

Kirk

### Re: Gearify

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.ArtF wrote: >>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?

...

Enjoy the vacation.

### Re: Gearify

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 elliptical 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. Originally, 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 involution from that point. Now all that was ,to my mind ,necessary to pick a start point for the involution to occur, but

as you stated it, calculating a running contact point up that line sounds better and easier, with no need to

figure the involution angles involved.. maybe..

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

I will and Ill try. But Ill fail. lol Thx

Art

>>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 elliptical 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. Originally, 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 involution from that point. Now all that was ,to my mind ,necessary to pick a start point for the involution to occur, but

as you stated it, calculating a running contact point up that line sounds better and easier, with no need to

figure the involution angles involved.. maybe..

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

I will and Ill try. But Ill fail. lol Thx

Art

### Re: Gearify

Hello!

Some of you may be interested to know that Gearify is developing a new tool for the generation of involute teeth on arbitrary pitch curves.

Teaser video can be seen here:

https://youtu.be/8aOFbEwis1w

I made an in depth mathematical analysis to understand how the constraints and degrees of freedom change at each point along the curve and made some intriguing discoveries.

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

-Gearify

Some of you may be interested to know that Gearify is developing a new tool for the generation of involute teeth on arbitrary pitch curves.

Teaser video can be seen here:

https://youtu.be/8aOFbEwis1w

I made an in depth mathematical analysis to understand how the constraints and degrees of freedom change at each point along the curve and made some intriguing discoveries.

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

-Gearify

### Re: Gearify

Looks good. Looks very similar as to how Gearotic does it, a digital subtraction where the involute evolves from the instantaneous rate of change during its construction? 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 contruction and elliptial coefficient. They look good though, generation seems smooth.

Art

depending on contruction and elliptial coefficient. They look good though, generation seems smooth.

Art