Talk:Involute

Re-writing required
The opening paragraph for this article is unnecessarily complicated and should really be rewritten —Preceding unsigned comment added by Owen214 (talk • contribs) 11:43, 23 August 2009 (UTC)

Polar Equations are not correct
The polar equations for the spiral don't look correct. For example, in polar coordinates the non-radial line that crosses the radial line  perpendicularly at the point (r0, φ) has the equation form $$r(\theta) = {r_0}\sec(\theta-\varphi)\,$$. This is the equation given here for the spiral. So there is an inconsistency here that must be addressed. -- 05:52, 22 January 2011‎ Kamin of Ressik


 * Hello, I was astonished to see that there was no reaction for such a long time. Now I have eliminated one formula (the one with "arctan"), which was not correct and quite impractical. I replaced it by another one which is simpler but uses the same parameter which I renamed to $$\tau $$ in order to avoid parameter collision with the "t" in the first parametrization which is used again in the following curve length formula.--Enyak (talk) 15:36, 2 March 2012 (UTC)

Comparison of Archimedean spiral vs. involute of circle
Made a direct comparison graphic... AnonMoos (talk) 14:41, 1 May 2012 (UTC)

The above graphic is seems inaccurate and misleading. While the two curves differ at theta=0, the archimedean spiral quickly approaches the involute curve as theta increases. See functions graphed here as example: https://www.desmos.com/calculator/avzknqdy9m The graphic from AnonMoos appears that they stay a fixed distance apart for some reason. — Preceding unsigned comment added by Peepsalot (talk • contribs) 22:37, 31 December 2017 (UTC)

Changes made by Lichinsol
The following recent changes by user Lichinsol should be removed: 1) The two common definitions (in the lead) should be seperated again, as it has been. 2) The first picture (parabola) should be inserted again. It is a preparation for the considerations below. 3) The variable w within the integrals should be introduced again. It has to be different from the boundary t. 4) I can not see any sence changing the name of the involute from C (like Curve) to Alpha. Now it doesn't comply with the diagram. --Ag2gaeh (talk) 13:07, 29 September 2019 (UTC)

Add.: "Parallel curves of a parabola are no parabolas !" is true. Please insert this sentence and the example "semicubic parabola" again. --Ag2gaeh (talk) 15:46, 29 September 2019 (UTC)
 * Please see my reverted edit. "Parallel curves of a parabola are no parabolas" is true, I understood it now. The two defintions in the introduction were the same, so no need for separation. If we use variable w it seems that the parameter of function is changed which seems inappropriate. The first picture of parabola was not useful and the involute of circle animation explains everything. The variable C and c are so alike they need to be distinguished.Lichinsol (talk) 16:11, 29 September 2019 (UTC)
 * Also a minor mistake in the image for(involute properties) was edited and fixed.Lichinsol (talk) 16:13, 29 September 2019 (UTC)


 * Add. to 3) The notation (double meaning of parameter t) $$\int_a^t|\vec c'(t)|\; dt $$ is just wrong. See any text book on calculus or here. --Ag2gaeh (talk) 17:00, 29 September 2019 (UTC)
 * I edited it with the correct notation. Thank u. Lichinsol (talk) 17:19, 29 September 2019 (UTC)


 * Please restore the original version, restrict Your editing to improvements of the text, but do not change mathematics without a discussion on this talk page. It is annoying to check all Your edits for flaws and mistakes.--Ag2gaeh (talk) 20:32, 29 September 2019 (UTC)
 * Every article on wikipedia is prone to changes. It is inevitable. No editor should claim to revert it just to the place where he dropped it just for the sake of selfishness. A new reader needs easier language and better explanations for easier grasping of concepts. As such there is no need for reverting to an older version-which lacks explanations. Any mistake in the present version must be scrutinized, and made better.Lichinsol (talk) 05:09, 30 September 2019 (UTC)

WP:BRD is clear: when an edit is disputed, the previous stable verstion of the article must be restored until a consensus is reached on the talk page. Here, the stable version has clearly some issues (for example, in the lead, the intuitive description and the mathematical formulation are wrongly presented as different definitions), but a large part of 's edits is controversial. For example, in the lead, a definition is presented that is highly confusing: it presents as a property a part of the definition (length property), and as a part of the definition a property (normal property). Also this definition is circular, as it uses a property of the involute for defining it. Another controversial edit is the introduction of an animation in the lead: many readers find such an animation as distracting when there is no way of stopping it. Therefore animations are rarely accepted in the lead of a mathematical article.

Therefore, I'll restore the old version. Please do not do possibly controversial edits without a consensus here. D.Lazard (talk) 08:49, 30 September 2019 (UTC)


 * Some things I am mentioning about the old version:
 * The lead two definitions must be united to one.
 * There has to be a clean explanation of the formula in section "Involute of a parametrized curve".
 * The image having description "Involute, properties" has a mistake. Ca, C0 as the names of the curve must be replaced with each other.
 * In the "Examples" section, displaying Result separately is a redundancy, which was already written in the previous line.
 * In example of "involutes of a circle", if arc length formula is shown, then a short derivation of it must be shown, or else it must be removed.
 * Lastly, it would be better if an explanation for (Parallel curves of a parabola are not parabolas anymore!) is given to the readers. An unneeded sentence regarding the extending of string by a length is given in the section "Involute of a parameterized curve" which can confuse a new reader. Its existence should be limited to the example where it is used(in semicubic parabola).Lichinsol (talk) 13:23, 30 September 2019 (UTC)
 * The definitions of the lead must not be merged. The first one is "informal [...], without rigor, suitable for a general audience", as recommended in MOS:MATH. The second is a mathemtical translation of the first one. I am not sure that it belongs to the lead. IMO, it would be better placed at the beginning of section "Involute of a parameterized curve", as it explains the formula which, presently, is given without any explanation.
 * Some redundancy is sometimes useful. Instead of displaying the result at the end, it would be better (for people who are not interested in proofs) to say at the beginning of each subsection something like "for this curve, the involute starting from this point is that; the other involutes are more complicated but can be described as the curves parallel to this particular involute.
 * For the parallels to a parabola, one may link to parallel curve, where it is said that the parallels to a parabola are algebraic curves of degree 6 (it is there that a reference should be added)
 * I agree that the article has many issues. You may fix them yourself, but, please, only one at a time, and with an edit explaining clearly this edit. Proceeding like that is the right way for not being reverted for edits that improve the article. D.Lazard (talk) 15:38, 30 September 2019 (UTC)

Re-writing of the lead, and addition of derivation for the formula
The present version of the lead section has the problem of redundant text and unrequired lines which do not belong to the lead. Please see my edits(dated 10:04 1 Oct 2019, and 10:42 1 Oct 2019) which were reverted. The edits are my proposal for the upgradation of the page. Required, the agreement of whoever sees this message.Lichinsol (talk) 13:23, 1 October 2019 (UTC)

I must suggest to not revert any edit if there are no issues in it. New data must be added to wikis. You must read WP:BRD again. It does not suggest rash reverting. Revert only when there is problem in the edit.Lichinsol (talk) 13:46, 1 October 2019 (UTC)
 * There are a lot of problems in your edit of the lead:
 * It removes the short description that must be in every article, see WP:Short description
 * It introduce roulettes as soon as of the second paragraph of the lead. This must be avoided per WP:TECHNICAL, as a reader is not supposed to know of roulettes for reading the article.
 * It involves several sections, which makes difficult for other editors to review the changes.
 * It introduces in the second section a paragraph beginning by "The string", when there is no string earlier in this section.
 * It does not distinguish between the non-mathematical intuitive description with a string (a string is not a mathematical object) and the mathematical description through tangents and arc length. I agree that this is a little confusing in the previous formulation and that the matematical definition needs improvement, but there was at least a tentative of a mathematical definition, which is completely lacking in your version.
 * Each of these items would be a valid reason for reverting. In the whole, your version does not follow the guidelines of the manual of style and is not mathematically better than the previous version. D.Lazard (talk) 14:15, 1 October 2019 (UTC)
 * I apologize but it seems u are making points which dont have weight. You probably dont like someone editing wikipedia except u ruling and crossing them all the time.
 * You must read the following articles I write here (only the intro) and count how many "roulettes" type of problems u see: Heat, State Function, etc.
 * I dont seem that there is a need to justify your every bullet point.Lichinsol (talk) 14:24, 1 October 2019 (UTC)
 * Add: Dont give excuses of WP:blah_blah unless it is really necessary.Lichinsol (talk) 14:25, 1 October 2019 (UTC)
 * Add: I respect u, and every other editor. Your contribution to wikipedia has been immense. But u must cooperate with the others who make an effort. If there are problems edit them, dont revert.Lichinsol (talk) 14:29, 1 October 2019 (UTC)

Gears - not correct?
"Their relative rates of rotation are constant while the teeth are engaged. The gears also always make contact along a single steady line of force. "

My understanding (from watching Clickspring) was that cycloidal gears give a constant rate of relative rotation and so are used in clocks, whereas involute gears have the straight line of force (it's not "steady", it's straight) and are used in load-bearing machinery.

203.13.3.93 (talk) 00:03, 30 August 2022 (UTC)


 * Good catch -- I hopefully made the text a bit more straightforward. Both involute gear and cycloid gear have articles, and both follow the fundamental law of gearing, which means that as long as everything keeps working correctly (contact and torque is maintained without discontinuities, etc.) the ratio of angular momentums of meshed gears should be constant. Beyond that, this is far from my specialty. SamuelRiv (talk) 03:15, 30 August 2022 (UTC)