"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 discovered the previously unknown, or at least unpublished attribute of the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