Talk:Epicyclic gearing

message: OK, it's about time we got some examples of how the gear ratios work in this thing. Preferably a version that is easy to understand for the non-mathematician (namely, me). I found this site that attempts an explanation, but it leaves me somewhat baffled. Ideally, a thorough exposition of how the ratios are calculated would be nice, but a simple formula would suffice for now. Three cases:
* Annulus (outer ring) fixed
* Planetary carrier fixed
* Sun gear fixed
In each case, what is the ratio between the remaining gearsets, in simple terms of how many teeth each gear has? For the second case, it's fairly easy, since the sun and annulus simply turn in opposite directions, in the ratio sun/annulus = -teethannulus/teethsun (this is our reverse gear, as mentioned above). For the others, there's some angular velocity of the carrier involved, which taxes my brain. Assistance would be welcome. -- Wapcaplet 00:41, 23 Jul 2004 (UTC)
thread_title:  My math is rusty 

message: Animated gifs, showing each locking configuration would be very helpful - its very difficult to visualise this kind of thing.
:would this be any good? just the pic in the article now put together --Astrokey44 13:47, 26 May 2006 (UTC)
replies: text: I like it.  It would be even better with an intermediate frame; a little easier to follow. ike9898 22:45, 12 June 2006 (UTC)
replies: text: Is it possible to do this with photoshop? When I try to do tweening the in between frame only changes the opacity of the two not the position --Astrokey44 12:33, 22 June 2006 (UTC)
thread_title:  Animated gifs 

message: To me, this article feels incomplete.  I would expect to see a discussion of the advantages/disadvantages of planetary gears versus other gearing arrangements (i.e. when would you want to use planetary gears? when would you not?)  For example, advantages include high power density, large reduction in a small volume, multiple kinematic combinations, pure torsional reactions, coaxial shafting.  Disadvantages include high bearing loads, inaccessibility, design complexity.  I have studied planetary gears in graduate school and could add such a section if others think it would add value...  This would be my first attempt at contributing to wikipedia so I wanted to test the waters before jumping in...
Kiracofe8 02:51, 6 February 2007 (UTC)
thread_title:  possible addition: advantages/disadvantages  

message: I'd say this article is lacking the history of the epicyclic gear and the application of the gear. GraemeLeggett (talk) 12:15, 26 August 2009 (UTC)
thread_title:  Missing 

message: (First, I am harmless).
In the page on epicyclic gears, one section calls the annulus the ring gear. Either is correct but at least stick to one.
Malcolmcochran@hotmail.com  —Preceding unsigned comment added by 86.137.178.200 (talk) 11:58, 9 September 2009 (UTC)
replies: text: I've converted them all to annulus. Thanks for the heads up. Wizard191 (talk) 15:48, 9 September 2009 (UTC)
thread_title:  terminology 

message: Although not essential, the image seems a bit weird, ie the carrier design is not really standard, see the image at http://www.mvwautotechniek.nl/Motor/Transmissie/automatisch.htm
M. van Wijk 14:01, 22 March 2016
: There is no "standard design" for planet carriers. They're all correct. Do not be tempted to invent another of your "fixes". Andy Dingley (talk) 17:43, 13 December 2010 (UTC)
thread_title: Image

message: This article should be called planetary gearing because planetary gear-trains are just a specific instance of epicyclic gear-trains and there are many other configurations of epicyclic gear trains, for example a differential gear-train.  — Preceding unsigned comment added by Cdhickam (talk • contribs) 23:46, 29 March 2011 (UTC)
thread_title:  Article should be called planetary gears, not epicyclic gears. 

message: Is it possible to have the section on formulas protected, som that edits like this/vandalism will be prevented? Keanu (talk) 08:43, 6 May 2011 (UTC)
thread_title: Protection

message: The first two (seminal; general) gear ratio equations in the section
https://en.wikipedia.org/w/index.php?title=Epicyclic_gearing&action=edit§ion=3
do not appear to originate from the cited work [6]: L. Meirovitch: Elements of Vibration 
Analysis, McGraw-Hill, New York, 1986.(?) I would appreciate any assistance locating their 
origin(s) so it(they) may be correctly (and/or more specifically) cited - important not only for correctness here, but for readers wishing to trace the more complex / powerful methodologies / models by which they were obtained. 100kWhr (talk) 15:57, 9 October 2017 (UTC)
replies: text: Thank you for spotting this.  I have made the correction. Prof McCarthy (talk) 04:28, 10 October 2017 (UTC)
replies: text: Thank you Prof McCarthy for your rapid response. I have scanned [1] J. J. Uicker, G. R. Pennock and J. E. Shigley, 2003, Theory of Machines and Mechanisms, Oxford University Press, New York, and alas, cannot find direct or (obviously) implicit reference(s) therein, to these equations (or the means by which they were derived). 100kWhr (talk) 10:52, 10 October 2017 (UTC)

text: Correction: delete/disregard "(or the means by which they were derived)", [the cited reference covers basic kinematics, sufficient familiarity with which allows the reader to derive the equations].100kWhr (talk) 14:01, 15 October 2017 (UTC)

text: Ref.: Willis R, Principles of Mechanism, Cambridge University Press, 1841, Art. 406 ("By Epicyclic Trains"), pp 361-393, contains derivations of the epicyclic gear train ratios from a simple two gear train basis, up. The equations in question are not given, however they almost immediately fall out of Willis' derivations. As such, may I propose this old text be co-cited?100kWhr (talk) 20:47, 15 October 2017 (UTC)
thread_title: Citation

message: I've deleted the formulas section, because a lot of these formulas are incorrect (at least 7b and 8b are, and probably more). This should be checked upon! I don't have time to do this right now but I think no formulas is better than wrong formulas so I deleted them all. Here they are for future notice:
(I will see if I can get back on this, but I'm leaving on a vacation in a few hours)
  Notations of planetary gearing elements for the next table Pattantyús Gépész- és Villamosmérnökök Kézikönyve 3. tom. Műszaki Könyvkiadó, Budapest, 1961. p.632. 
Name                                   	Number of teeth       	Speed
{\color{blue} Driving} \,              	{\color{blue} z} \,   	{\color{blue} n} \,
{\color{magenta} Auxiliary\ driving} \,	{\color{magenta} z} \,	{\color{magenta} n} \,
{\color{red} Driven} \,                	{\color{red} z} \,    	{\color{red} n} \,
Fixed \,                               	z \,                  	n \,
{\color{green} Planetary} \,           	{\color{green} z} \,  	{\color{green} n} \,
{\color{cyan} Planetary} \,            	{\color{cyan} z} \,   	{\color{cyan} n} \,
  Sketch and output speed of planetary gearings 
Sketch	Output speed                                                                                                                                            	Sketch	Output speed                                                                                                                                            	Sketch	Output speed                                                                                                                                                                   	Sketch	Output speed
      	{\color{red} n} = {\color{blue} n} (1 + \frac {z}{\color{red} z})                                                                                       	      	{\color{red} n} = {\color{blue} n} (1 - \frac {z}{\color{red} z})                                                                                       	      	{\color{red} n} = {\color{blue} n} (0 + \frac {z} {\color{red} z})                                                                                                             	      	{\color{red} n} = {\color{blue} n} (\cos \beta + \frac {z}{\color{red} z})
      	{\color{red} n} = {\color{blue} n} (1 + \frac {{\color{green} z}z} {\color{cyan} z \color{red} z} )                                                     	      	{\color{red} n} = {\color{blue} n} (1 + \frac {{\color{green} z}z} {\color{cyan} z \color{red} z} )                                                     	      	{\color{red} n} = {\color{blue} n} \frac {1}{(1 + \dfrac {{\color{green} z}z} {\color{cyan} z \color{blue} z} )}                                                               	      	{\color{red} n} = {\color{blue} n} \frac {1}{(1 + \dfrac {{\color{green} z}z} {\color{cyan} z \color{blue} z} )}
      	{\color{red} n} = {\color{blue} n} (1 + \frac  {z} {\color{red} z}  )                                                                                   	      	{\color{red} n} = {\color{blue} n} (1 + \frac  {z} {\color{red} z}  )                                                                                   	      	{\color{red} n} = {\color{blue} n} \dfrac{1}{1 + \dfrac {z} {\color{blue} z}}                                                                                                  	      	{\color{red} n} = {\color{blue} n} \dfrac{1}{1 + \dfrac {z} {\color{blue} z}}
      	{\color{red} n} = {\color{blue} n} (1-\frac {{\color{cyan}z}z} {{\color{green}z} {\color{red}z}})                                                       	      	{\color{red} n} = {\color{blue} n} (1 - \frac  {z \color{green} z} {\color{cyan} z \color{red} z})                                                      	      	{\color{red} n} = {\color{blue} n} (1 - \frac  {z \color{green} z} {\color{cyan} z \color{red} z})                                                                             	      	{\color{red} n} = {\color{blue} n} \dfrac {1}{1 + \dfrac {z} {\color{blue} z}}
      	{\color{red} n} = {\color{blue} n} \dfrac  {1} {1- \dfrac {{\color{cyan}z} z} {{\color{green}z} {\color{blue}z}}}                                       	      	{\color{red} n} = {\color{blue} n} \dfrac  {1} {1- \dfrac {{\color{cyan}z} z} {{\color{green}z} {\color{blue}z}}}                                       	      	{\color{red} n} = {\color{blue} n} (1 - \frac  {z \color{green} z} {\color{cyan} z \color{red} z})                                                                             	      	{\color{red} n} = {\color{blue} n} (1 - \frac {{\color{green} z}z} {\color{cyan} z \color{red} z} )
      	{\color{red} n} = {\color{blue} n} \left[1-\left( \frac  {\color{magenta} n} {\color{blue} n} -1  \right)  \frac{\color{magenta}z} {\color{red}z}\right]	      	{\color{red} n} = {\color{blue} n} \left[1-\left( \frac  {\color{magenta} n} {\color{blue} n} -1  \right)  \frac{\color{magenta}z} {\color{red}z}\right]	      	{\color{red} n} = {\color{blue} n} \frac {1 + \dfrac  {\color{magenta} n \color{magenta} z} {\color{blue} n \color{blue} z}} {1 + \dfrac  {\color{magenta} z} {\color{blue} z}}	      	{\color{red} n} = {\color{blue} n} \frac {1 + \dfrac  {\color{magenta} n \color{magenta} z} {\color{blue} n \color{blue} z}} {1 + \dfrac  {\color{magenta} z} {\color{blue} z}}
:Specify which formulas are incorrect so they can be corrected. 7b and 8b, which ones are these? Dont delete something and then "leave for a vacation". I have reverted your deletion. Keanu (talk) 10:53, 15 July 2011 (UTC)
replies: text: Thanks. I think we will need some good references before we can use these formulas in the article. Keanu (talk) 15:45, 26 September 2012 (UTC)
replies: text: If 10a and 10b are wrong, and 10a and 13 are the same, along with 10b and 9, why don't we delete 10a and 10b? --  :- ) Don 16:07, 26 September 2012 (UTC)
replies: text: Do you have a reference to a trusted source that may confirm that the formulas are correct? I would like to check for myself before adding them to the article. Keanu (talk) 13:06, 1 October 2012 (UTC)
replies: text: No, I don't. Not into ME much, but I might be, the math is much more interesting that EE.  Forget my previous question, I now realize it was stupid.  But, are not 1, 2 and 3 identical?  I will put a reference book on my list, but finding all this in one reference is not likely. If I might make a suggestion to reduce some confusion to me and perhaps others, the drawings (which are very nice) are never going to do well in B&W, so maybe we could put the grey levels at the same point by darkening the green and eliminate two blues by changing the light blue to maybe orange?  The shading could be a light grey. Or at least make the coupling gear dark blue and light blue?  --  :- ) Don 14:46, 1 October 2012 (UTC)
replies: text: Yes, I do have a good source, and being a backyard tinkerer I personally built each system, as well as several other configurations I hopefully will make a graphic for to replace this one.  Here is the website I obtained the formulas from, http://www.roymech.co.uk/Useful_Tables/Drive/Epi_cyclic_gears.html  I agree that formulas 10a and 10b should be deleted, and posit that 3 and 12b should be deleted as well, since both are redundant as well.  3 being a special and easily solved case of 4a, and 12b being the same as 12a.  Before I mend the graphic for that, I'd like to be sure others agree with my justification.  — Preceding unsigned comment added by 97.124.82.32 (talk) 06:00, 3 October 2012 (UTC)
thread_title: Formulas for calculating gear ratios

message: It would be nice if it gave an intuitive explanation for the basic operation of increased rotation. With the sun gear held stationary, and carrier rotated, the annulus will spin faster. My intuitive explanation is that at any moment each planetary gear is like a tiny lever, with the fulcrum resting on a sun gear tooth, the effort at the center of the planetary gear, and the load at an annulus tooth. Clearly, this configuration increases motion of the load.
Also, the gear ratio section has an example with the carrier held stationary. It shows the ratio of the sun gear to a planetary gear, but this seems irrelevant; just the number of teeth on the sun and annulus matter. The planetary gears essentially "move" the sun gear closer to the annulus so it's as if its teeth were touching the annulus directly (except moving in the opposite direction). For every tooth of the sun gear that moves past a line from the center outward, one tooth of the planetary gear moves past the same point where this line intersects the annulus. I see that it eventually shows this with math. I'd like more "intuitive" explanations like this. 72.48.75.131 (talk) 19:55, 19 December 2011 (UTC)
thread_title:  Intuitive explanations? 

message: Hold on, the wikipedia article on the  Antikythera mechanism says that the device was definitively found not to contain any planetary gear mechanisms, and this was realized over a decade ago.  Why does this page contradict the other wikipedia page?
I think we ought to take down the reference to the  Antikythera mechanism on this page.  — Preceding unsigned comment added by 50.131.61.86 (talk) 11:46, 19 September 2013 (UTC)
replies: text: It doesn't contain any planetary gear systems (I suppose, I'm not 100% on the definition), but does contain an epicyclic set of gears.  Picture two gears mounted face to face, but on different axes (that is, there is an offset between the axes).  As the gears aren't meshed, they're free of each other.  Now put a pin on one that engages in a slot on the other such that the slot is positioned radially and is large enough to contain the full travel of the pin (that length is equal to the distance between the gear axes) through an entire revolution. Now, when one gear is driven at and even angular velocity, the other will speed up and slow down relative to the even velocity because its point of being driven moves radially across the gear.  The speed of the variable gear averages the same as the driver.  The Antikythera Mechanism used such a pair of epicyclic gears to model the ellipticity of the moon's orbit, and it even mounted the two gear on a gear that rotated once every 9 years of simulated time to model the elliptical precession of the moon.  Of course, the Greeks didn't see it as ellipticity, that had to wait for Kepler.  But they weren't as much into why as they were into making the model track with reality.  It is possible, but not certain, that the mechanism may have used other pin/slot epicycles to model the retrograde orbits of the other planets. SkoreKeep (talk) 07:10, 17 June 2014 (UTC)
thread_title:  History 

message: At the end of par. Gear Ratio, I've added an argument that I think is simple, intuitive and precise,
establishing the general formula that relates the angular velocities of sun, carrier and annulus
(plus two standard applications).
This might cause other explanations superfluous, but I made no further changes.KeesDoe (talk) 21:57, 27 March 2015 (UTC)
replies: text: Your intuitive explanation is correct but it duplicates the material provided in the following section.  Your "imagine a you are riding on the carrier" is the exactly the principle of the "fixed carrier train ratio."  You proceed to obtain the same equation included in the relationship of speed averaging of a differential, all of which are shown in the following section. Prof McCarthy (talk) 02:21, 31 March 2015 (UTC)
replies: text: Dear prof McCarthy, yes, I have been duplicating. The point is I find both arguments in the article incomprehensible and my aim was to add one that would be simple as well as precise. I hope most readers will find the existing exposition, like you, illuminating. (In view of this talk, I have doubts.) Anyway - thank you!KeesDoe (talk) 19:58, 1 April 2015 (UTC)
thread_title: Intuitive explanation!

message: I've made some animated gifs and some schematics that might help in this article. 
File:Planetary gear with fixed sun gear.gif|A planetary gear set where the sun gear is fixed
File:Planetary gear set schematic.svg|Planetary gear set schematic
File:Planetary gear set schematic fixed sun.svg|Planetary gear set schematic fixed sun
There is a full list on my profile page => DaveRcWiki (talk) 21:38, 5 February 2024 (UTC)
thread_title:  Animated gifs and schematics.  

message: For some of us who have been studying planetary gear trains for over 5/8 of a century, this article has several problems.  The first is that in the United States, the correct title should be Planetary Gear (Train). The USPTO classification is:  Class 475 PLANETARY GEAR TRANSMISSION SYSTEMS OR COMPONENTS. "Epicyclic" seems to be the term that is preferred in England.  However, unless there is a circular fixed sun gear, with circular planets in the same plane, (none of which are required), there are no points that trace out an epicycle.
The rest of the definition is not general.  It only describes one of the most simple types.  The main definition should say that "a planetary gear train has some gears whose axes are not fixed, but move in relation to the movements of the gears in the train".
The very first line says "is a gear reduction assembly".  A planetary gear train can be used for increase as well as reduction.  One of the most widely used planetary gears in the world, with millions of units in daily use, is the bicycle 3-speed hub.  It can decrease the speed to 75%, or increase it to 133 1/3 %, or leave it unchanged, the three being selected by various ratchet pawls.  agb 173.233.167.50 (talk) 18:38, 29 April 2024 (UTC)
thread_title:  First things