Talk:Peaucellier–Lipkin linkage

=name?= The article cites a book by Coxeter. Another book by Coxeter, Introduction to Geometry, Wiley, 1969, p. 83, gives Peaucellier's name as A. Peaucellier rather than C.N. Peaucellier.--76.167.77.165 (talk) 04:33, 14 April 2009 (UTC)

=wrong picture?= How could point B ever get to point O, if AB is smaller than AO? — Preceding unsigned comment added by 118.90.128.38 (talk) 21:54, 6 July 2011 (UTC)


 * It cannot. But in normal operation, it doesn't need to.  This linkage was designed purely to allow the piston rod of a steam engine to move in a perfectly straight line.  This is achieved with point B describing a circle centred on the pivot point which is exactly midway between O and B.  Although the described circle will pass through point O, point B can never actually do so.  The system can only work as long as points A and C do not become coincident. DieSwartzPunkt (talk) 16:43, 23 October 2011 (UTC)

The animation shows the straight line action, but point o and b are shown as fixed, but point b is described in the text as following the circle. — Preceding unsigned comment added by 12.151.93.2 (talk) 18:18, 24 May 2012 (UTC)

Not true rotary motion to linear!
So my issue is that the PLL does not convert a whole rotation into linear motion. Strictly speaking this is converting a curved oscilation to a straight line oscilation.

DrBwts (talk) 21:17, 7 July 2014 (UTC)

= Revised formulas =

The formulas on this wiki article appear quite disorganised, appearing to rely on each other and may encourage people to disregard them completely instead of using them to design a linkage. So, I have decided to see which lengths are least important and make new formulas to allow the engineer to specify the values for the more important lengths. This also lets us see which mathematical associations are missing at this time.

Lets start:

1. Decided to specify OD, it is the total length.

2. Also specifying k because it effects the output vertical line amplitude, according to diagram on wiki page
 * There are no amplitude/reach formulas provided, once they are, k can be determined by specifying an output amplitude in association with h

Rules from existing formulas:
 * When OA and AD come together (one subtracting), y and x is associated or k is associated, but there is no h
 * AD is associated with x and h
 * OA sees x,h and y
 * when either OA or AD comes, h also comes, so I have to specify one of these three.

3. Decided to specify h, for linkage height and leverage
 * now AD and then OA can be determined.
 * Need a formula to specify a leverage, if more convenient than h.


 * {| class="toccolours collapsible collapsed" width="90%" style="text-align:left"

!See the calculations used to come to my conclusions k is circle origin to B; BP or PD is x; OB is y; AP is h and also: OD is L; OA is Z and AD is N

To get y from existing formulas: $$yL=k^2$$ thus $$y=k^2/L$$

To get x from existing formulas: $$k^2= y^2+2xy$$ and $$k^2-y^2=2xy$$ thus $$x=(k^2-y^2)/(2y)$$

To get N from existing formulas: $$N^2=x^2+h^2$$ thus $$N=\sqrt{x^2+h^2}$$

To get Z from existing formulas: Either, $$Z^2-N^2=k^2$$ thus $$Z=\sqrt{k^2+N^2}$$, or, $$Z^2=(y+x)^2+h^2$$ thus $$Z=\sqrt{ (y+x)^2+h^2 }$$


 * }

So we still need formulas for linkage reach and leverage.

Also note, image PeaucellierApparatus.PNG is missing k, from the circle origin to B. Please note that there has not been any linkage designed from these formulae, so I am not sure of OD is at its longest point or its shortest.Charlieb000 (talk) 03:50, 28 June 2016 (UTC)

Original texts
Could there be a reference to the original publications by Peaucellier and Lipkin, with their dates of publication? I saw a mention of Peaucellier in an old book, and wanted to follow it up. The independent discovery by Lipkin is new to me. I followed through the links in notes 1 and 2 to the present article, but they do not lead to anything useful.2A00:23C5:6487:4701:9999:86EF:FF4F:185 (talk) 18:33, 27 June 2020 (UTC)

Suggestions for expanding this article
I originally had two, after reading "(talk) 21:17, 7 July 2014 (UTC)" above I have three suggestions.

First, has this linkage ever been generalized so that Point B travels in a complete circle (some bars will have to be in different planes to allow Point B to pass over Point O without being blocked by it) and while Point B's travel is never reversed that are points on B's circular path that map to extremes of the straight-line path of Point D, these being the places on Point B's circle where the straight-line motion is reversed?

Second, can we conceive of this linkage as being a special case (the case where rods OA and OC are all of the same length, and the four rods AB, BC, CD, and DA are all of some other length) of the same linkage where there are no constraints on the lengths of the bars? Has the theory that explains the straight-line output of moving Point B in a circle be generalized to predict the result of ANY combination of lengths of the various rods? In other words, if you change the lengths of various rods, do you get an output at Point D that is not a straight line but is some other interesting shape?

Third, I don't think (but did I just miss it?) that this article contains a statement as to whether the length of the line traced by Point D (for a given arc traveled by Point B) is or is not always proportional to the length of the arc traveled by Point B.2604:2000:1383:8B0B:1C64:8308:33BC:E2D6 (talk) 22:44, 9 October 2020 (UTC)Christopher L. Simpson