Generalized gears: Difference between revisions
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* only solved for cycloid profiles though and | * only solved for cycloid profiles though and | ||
* not for evolvent or other profiles. | * not for evolvent or other profiles. | ||
== Precise implementation == | == Precise implementation == | ||
See referenced papers. <br> | See referenced papers. <br> | ||
{{Wikitodo|Get OpenSCAD implementation working. Publish, and link to it from here.}} | {{Wikitodo|Get OpenSCAD implementation working. Publish, and link to it from here.}} <br> | ||
{{wikitodo|Implementation details so far understood.}} | |||
== Imprecise naive approach == | == Imprecise naive approach == | ||
| Line 56: | Line 55: | ||
== References == | == References == | ||
=== Winfough2014 === | === Stachel2020 (open access) === | ||
Recalling Thread Constructions of Quadrics∗ <br> | |||
https://www.heldermann.de/JGG/JGG24/JGG242/jgg24011.htm <br> | |||
https://www.heldermann-verlag.de/jgg/jgg24/j24h2stac.pdf <br> | |||
https://repositum.tuwien.at/handle/20.500.12708/141879 <br> | |||
=== Winfough2014 (open access) === | |||
W. R. Winfough and D. B. Dooner, "Testing of Alternative Spiral Bevel and Hypoid Gear Theory", Power Transmission Engineering, August 2014, pp. 30-36. | W. R. Winfough and D. B. Dooner, "Testing of Alternative Spiral Bevel and Hypoid Gear Theory", Power Transmission Engineering, August 2014, pp. 30-36. | ||
| Line 70: | Line 76: | ||
Giorgio Figliolini, Jorge Angeles, "The Synthesis of the Pitch Surfaces of Internal and External Skew-Gears and Their Racks", Journal of Mechanical Design, Vol. 128, No. 4, pp. 794–802, July 2006. | Giorgio Figliolini, Jorge Angeles, "The Synthesis of the Pitch Surfaces of Internal and External Skew-Gears and Their Racks", Journal of Mechanical Design, Vol. 128, No. 4, pp. 794–802, July 2006. | ||
https://doi.org/10.1115/1.2202875 [https://web.archive.org/web/ | https://doi.org/10.1115/1.2202875 [https://web.archive.org/web/20250117204445/https://asmedigitalcollection.asme.org/mechanicaldesign/article-abstract/128/4/794/471910/The-Synthesis-of-the-Pitch-Surfaces-of-Internal?redirectedFrom=fulltext via internet archive] | ||
== People & institutions == | == People & institutions == | ||
Latest revision as of 09:31, 30 June 2025
There is a completely general way to generate/synthesize gear pairs …
- for any combination of axes and
- for positive nonzero whole number gear ratios.
Rotation axes can come in any possible combinations (except identical):
- parallel (spur gear pairs)
- antiparallel (spur gear in ring gear)
- angleled and crossing (conical bevel gears)
- angled and not crossing (hyperboloid gears)
This gear synthesis method is stated to only be …
- only solved for cycloid profiles though and
- not for evolvent or other profiles.
Precise implementation
See referenced papers.
(wiki-TODO: Get OpenSCAD implementation working. Publish, and link to it from here.)
(wiki-TODO: Implementation details so far understood.)
Imprecise naive approach
Factoring the tooth profiles apart from the rolling surface.
First: Modelling the teeth profiles as a rack (cycloidal or trapezoidal)
modeling it highly subdivided even for flat surfaces.
Second: Doing for all the vertices simply a coordinate transformation to
the rolling surfaces given as a coordinate system with
x & y on the spanning the rolling surface z normal to it for the local tooth profile height.
Consequences:
Note that mapping a strait-flank trapezoidal rack to a cylindrical coordinate systems
maps the straight flanks to pieces of archimedian spiral (i.e. radius growing linear with angle).
And these are only a decent approximation for true evolventsfor rarge gears with many teeth.
The stiffer the material the less forgiving.
- Would be very bad for steel. Long range transmitted vibrations at turning frequency times tooth number + overtones.
- Is bad for many 3D printed plastics as most are quite stiff.
- May in some cases be acceptable for nanoscale atomically precise gears as
atomic interactions are not so much like sharp surfaces.
Especially since the atomistic granularity might cause bigger deviations from the ideal shape anyway.
(wiki-TODO: Publish cleaned up existing OpenSCAD implementation and link to it from here.)
(wiki-TODO: Add illustrative demo image of results.)
Related
External links
References
Stachel2020 (open access)
Recalling Thread Constructions of Quadrics∗
https://www.heldermann.de/JGG/JGG24/JGG242/jgg24011.htm
https://www.heldermann-verlag.de/jgg/jgg24/j24h2stac.pdf
https://repositum.tuwien.at/handle/20.500.12708/141879
Winfough2014 (open access)
W. R. Winfough and D. B. Dooner, "Testing of Alternative Spiral Bevel and Hypoid Gear Theory", Power Transmission Engineering, August 2014, pp. 30-36.
https://www.powertransmission.com/testing-of-alternative-spiral-bevel-and-hypoid-gear-theory via internet archive
https://ik.imagekit.io/agmamedia/issues/0814/spiral-bevel-gears.pdf via internet archive
Figliolini2013
Giorgio Figliolini, Hellmuth Stachel, Jorge Angeles, "On the Synthesis of Spatial Cycloidal Gears", Meccanica, Vol. 48, pp. 1239–1249, 2013. https://doi.org/10.1007/s11012-012-9664-9 via internetarchive
Figliolini2006
Giorgio Figliolini, Jorge Angeles, "The Synthesis of the Pitch Surfaces of Internal and External Skew-Gears and Their Racks", Journal of Mechanical Design, Vol. 128, No. 4, pp. 794–802, July 2006. https://doi.org/10.1115/1.2202875 via internet archive
People & institutions
Hellmuth Stachel
https://en.wikipedia.org/wiki/Hellmuth_Stachel
https://www.geometrie.tuwien.ac.at/stachel/
https://www.geometrie.tuwien.ac.at/
Giorgio Figliolini
https://dblp.org/pid/39/1517.html
https://www.researchgate.net/profile/Giorgio-Figliolini
https://ieeexplore.ieee.org/author/37727132100
Jorge Angeles
https://www.mcgill.ca/mecheng/people/faculty/staff/jorgeangeles
W. R. Winfough
https://www.scopus.com/authid/detail.uri?authorId=6507515209
D. B. Dooner
https://www.researchgate.net/scientific-contributions/David-B-Dooner-82040915
https://www.uprm.edu/inme/people/faculty/dooner-david-b/ via internetarchive