Hi

For those interested, here are the results of the discussion in the thread
https://news.povray.org/web.671f6067fcb28935402042d461a8e06%40news.povray.org

https://archive.geartechnology.com/view/8600970/50/

Thank you once again for your efforts! All the best.

Kind regards,
Igor

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"spigor" <nomail@nomail> wrote:
> Hi
>
> For those interested, here are the results of the discussion in the thread
> https://news.povray.org/web.671f6067fcb28935402042d461a8e06%40news.povray.org
>
> https://archive.geartechnology.com/view/8600970/50/
>
> Thank you once again for your efforts! All the best.

Dr. Zarebski,

I'm happy to see that everything worked out well for you.

Although I have been interested in the geometric, mechanical, and engineering
aspects of gears for some years, the level that you're operating at is of course
well beyond anything that I've explored in depth.

From a development standpoint, I'm wondering if you ran into any difficulties or
limitations with the present POV-Ray release, and if there were any mathematical
or geometric tools that would have helped you more easily accomplish your task.

And, just out of curiosity, how much more work would be required to fully model
a set of mating gears complete with teeth?  Because that would make a fantastic
animation!

I'm also glad to see that in the course of your inquiries and analyses that you
discovered the previously unknown, or at least unpublished attribute of the
hypoid gears having a contact stripe rather than simply a tangent line. Surely
that will be important for analyzing axle and gear stress, strain, and wear.

Wishing you all the best, and thank you for choosing, using, and mentioning
POV-Ray!

-Bill Walker



Here are my introductory-level gear projects:

https://news.povray.org/povray.binaries.images/thread/%3Cweb.56eb28497cd2ac6a5e7df57c0%40news.povray.org%3E/

http://news.povray.org/povray.binaries.images/thread/%3Cweb.593939a97ee89277c437ac910%40news.povray.org%3E/?ttop=419432
&toff=50&mtop=416421

https://news.povray.org/povray.binaries.images/thread/%3Cweb.5bde30bdb3e70712765e06870%40news.povray.org%3E/?ttop=44646
1&toff=800

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And now, through the magic of Sergei's online conversion tool,
I don't have to do any complex math.

Enjoy the hypoid gear set - wheel and pinion.

- BW

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Attachments:
Download 'hypoid.mpg' (1948 KB)

On 16/10/2025 02:40, Bald Eagle wrote:
> And now, through the magic of Sergei's online conversion tool,
> I don't have to do any complex math.
> 
> Enjoy the hypoid gear set - wheel and pinion.

Really nice !
But I'd prefer to see them rusty ).

Gears is my love since a childhood, my grandfather was a chief mechanic
of a heavy machine tool plant - I often saw machinery blueprints at
home and was enchanted by them. Now I have a small CNC (10x13 cm) and
play with it from time to time.

I am completely sure that you know this site:
https://geargenerator.com/
--
YB

Post a reply to this message

"Bald Eagle" <cre### [at] netscapenet> wrote:
> Dr. Zarebski,
>
> I'm happy to see that everything worked out well for you.
>
> Although I have been interested in the geometric, mechanical, and engineering
> aspects of gears for some years, the level that you're operating at is of course
> well beyond anything that I've explored in depth.
>
> From a development standpoint, I'm wondering if you ran into any difficulties or
> limitations with the present POV-Ray release, and if there were any mathematical
> or geometric tools that would have helped you more easily accomplish your task.
>
> And, just out of curiosity, how much more work would be required to fully model
> a set of mating gears complete with teeth?  Because that would make a fantastic
> animation!
>
> I'm also glad to see that in the course of your inquiries and analyses that you
> discovered the previously unknown, or at least unpublished attribute of the
> hypoid gears having a contact stripe rather than simply a tangent line. Surely
> that will be important for analyzing axle and gear stress, strain, and wear.
>
> Wishing you all the best, and thank you for choosing, using, and mentioning
> POV-Ray!
>
> -Bill Walker
>
>
>
> Here are my introductory-level gear projects:
>
>
https://news.povray.org/povray.binaries.images/thread/%3Cweb.56eb28497cd2ac6a5e7df57c0%40news.povray.org%3E/
>
>
http://news.povray.org/povray.binaries.images/thread/%3Cweb.593939a97ee89277c437ac910%40news.povray.org%3E/?ttop=4194
32
> &toff=50&mtop=416421
>
>
https://news.povray.org/povray.binaries.images/thread/%3Cweb.5bde30bdb3e70712765e06870%40news.povray.org%3E/?ttop=446
46
> 1&toff=800

Hello Bill
Thank you for your thoughtful message and for sharing your interesting projects
and insights.

My work with POV-Ray has gone smoothly; it seems almost tailor-made for such
illustrations due to its precise mathematical approach to description,
calculation, and rendering of cones and cylinders as lathe objects. It is a
wonderful tool, and I am grateful to all its creators.

In my opinion, fully modeling gear teeth would first require answering several
questions. If done purely for educational animation purposes, aesthetics matter
most while other factors take a back seat. I viewed the animation of the hypoid
gear assembly you sent, and it looks very good, so from that perspective, the
matter is likely settled.

However, if the modeling were to be used for highly accurate purposes, two areas
should be distinguished the active flank and the transition curve at the tooth
root. For flanks in the simplest involute cases parametric equations exist, but
here we are not talking about those. For flanks such as those in hypoid gears, a
unique geometry description method is the use of a point cloud with
corresponding normal vectors. So, it would be necessary to create an object that
uses such data as input and generates the surface accordingly.

Another known method is simulation of machining by calculating successive tool
positions in relation to the teeth and subtracting solids from each other.
Surfaces obtained this way tend to be stepped, not perfectly smooth, require
extensive computation, and very small angular differences at intersections can
cause unexpected effects.

Regarding the transition curve at the tooth root, this involves another set of
phenomena, which have been highlighted, for example, in
https://gearsolutions.com/features/transition-curve-much-more-than-a-radius-at-the-root-fillet-of-a-tooth/
If the modeling goal was solely animation, it would probably suffice to replace
it simply with a rounding.

There are software packages on the market that realize these tasks in various
ways, so before investing effort in new functionality, one should consider where
we would stand after creating it. A "hypoid gear modeling" query on YouTube
shows some interesting results.

About 20 years ago, for the Non-circular gear animation within the Travelling
Curves project, I used a height field object, but that approach has obvious
limitations.
https://news.povray.org/povray.binaries.animations/thread/%3C68f0002e%241%40news.povray.org%3E/
https://paulstgeorge.com/travelling-curves/index.html

I also want to say that I have found here a group of very interesting people,
many apparently passionate about gearing. I admire your achievements and believe
humanity can be proud of you.

I've noticed that collaboration among diverse communities can yield surprising
and beautiful results. A relative of mine, uncle Zdzisiek, an industrial
conveyor designer, used to say: "If something can't be done, give it to a
student. The student doesn't know it can't be done and will just do it."

For example, I had an industrial project in mind related to electromagnetic wave
simulation in an industrial setting. If of any interest, anyone wishing to
contact me directly can find me at the email starting with spigor and ending
with op.pl.

I wish you all the best!
Kind regards,
Igor

Post a reply to this message

On 17/10/2025 11:17, spigor wrote:
> About 20 years ago, for the Non-circular gear animation within the Travelling
> Curves project, I used a height field object, but that approach has obvious
> limitations.
>
https://news.povray.org/povray.binaries.animations/thread/%3C68f0002e%241%40news.povray.org%3E/
> https://paulstgeorge.com/travelling-curves/index.html

Can you please share the geometry of gears from 'Travelling curves' ?
They are so unusual and attractive - I would like to make online
real-time animations of them.

> For example, I had an industrial project in mind related to electromagnetic wave
> simulation in an industrial setting. If of any interest, anyone wishing to
> contact me directly can find me at the email starting with spigor and ending
> with op.pl.

Thank you for the invitation, I sent an email today.

With best wishes,
-- 
YB

Post a reply to this message

Dr. Zarebski,

> My work with POV-Ray has gone smoothly; it seems almost tailor-made for such
> illustrations due to its precise mathematical approach to description,
> calculation, and rendering of cones and cylinders as lathe objects. It is a
> wonderful tool, and I am grateful to all its creators.

Yes, it's pretty difficult to find something that's so suited to such geometric
tasks yet so accessible to anyone, free, and open-source as well.

"rendering of cones and cylinders as lathe objects"
I'm not sure if going that route gains you anything - cones and cylinders are
basic primitive shapes.
https://wiki.povray.org/content/Reference:Cone
But perhaps the shapes you're using don't have simple flat endcaps.

> I viewed the animation of the hypoid
> gear assembly you sent, and it looks very good, so from that perspective, the
> matter is likely settled.

Well that got modeled by
https://www.otvinta.com/download06.html
and I just wanted something that would clearly depict how the gears work, as
supplementary material to your article.

> For flanks such as those in hypoid gears, a
> unique geometry description method is the use of a point cloud with
> corresponding normal vectors. So, it would be necessary to create an object that
> uses such data as input and generates the surface accordingly.

That sounds to me like numerical methods are used to calculate the geometry, and
a mesh of triangles (perhaps the result of FEM) would be the preferred
embodiment of such data.

> Another known method is simulation of machining by calculating successive tool
> positions in relation to the teeth and subtracting solids from each other.
> Surfaces obtained this way tend to be stepped, not perfectly smooth, require
> extensive computation, and very small angular differences at intersections can
> cause unexpected effects.

Yes, I read a lot about that method when modeling very small gears, as it's
quite commonly used to provide an undercut for clearance of the larger gear's
teeth.

I used the same approach to "machine" the toolpath for the flutes of a twist
drill bit, and encountered everything that you mentioned above.

I'm tempted to suggest that a parametric curve ought to be able to describe the
tooth shape - perhaps a Coons patch for the tooth flank.  Presumably the stepped
tool path could be interpolated and thus provide a smoother result.


> Regarding the transition curve at the tooth root, this involves another set of
> phenomena, which have been highlighted, for example, in
>
https://gearsolutions.com/features/transition-curve-much-more-than-a-radius-at-the-root-fillet-of-a-tooth/

Yeah - I have dealt with stress risers and the consequences of inadequate tooth
strength.  I opened up a manual transmission, and a pile of sheared off teeth
just poured out.  (oof.)

> If the modeling goal was solely animation, it would probably suffice to replace
> it simply with a rounding.

Well, yes.  Graphics and engineering are vastly different fields.
I recall reading a quote attributed to Archimedes about art vs math (which I
have since been unable to find again)
It was basically the observation that in art, one can do whatever one wants, but
with math, there are rigorously enforced rules.
(And having known many artists, they are prone to just do whatever and then
rationalize the result after the fact)


> I also want to say that I have found here a group of very interesting people,
> many apparently passionate about gearing. I admire your achievements and believe
> humanity can be proud of you.

Gears are what lie between accomplishing our useful tasks, and Ayn Rand's engine
that drives the world.
And hypoid gears are what drive most heavy vehicles in the rear differential.

Are you familiar with Brandon Sander of Inheritance Machining?
He recently tried to machine some gears, and could probably use some expert
advice from someone of your caliber.
https://www.youtube.com/watch?v=sQ_blQAkC4Y

> I've noticed that collaboration among diverse communities can yield surprising
> and beautiful results. A relative of mine, uncle Zdzisiek, an industrial
> conveyor designer, used to say: "If something can't be done, give it to a
> student. The student doesn't know it can't be done and will just do it."

I agree, and have made the same point.  And I will point out that we both know
the real meaning of "just".  ;)

> For example, I had an industrial project in mind related to electromagnetic wave
> simulation in an industrial setting. If of any interest, anyone wishing to
> contact me directly can find me at the email starting with spigor and ending
> with op.pl.

I can't say that I could help, but I'm interested in hearing about it.  :)

Also, are you familiar with Paul Nylander?
http://www.bugman123.com/Physics/index.html

> I wish you all the best!
> Kind regards,
> Igor

Thank you,
for the kind words, and for sharing the results of your work.

- BW

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Bill,
Thank you so much for your deep insights and very interesting links. At first
glance, it looks like there are tons of incredible things there. I will
definitely explore them further when time permits.

I agree with all your points, which doesn't happen very often.

I'm not sure if free hobbing could ever work, but what about using two
sprockets, a chain, and a tensioner?

I'll get in touch about that industrial EM simulation idea, and I'm eager to
see what comes of it.

Ever so,
Igor

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