Straight-line mechanism (in Meccano, with a little mystery)

With a wonderfully descriptive title, the 1924 Dutch edition of Meccano Book 1 contains a straight-line mechanism; 'a device to convert a circular motion into a rectilinear motion'.

In English with a more abbreviated title, this same model here also in a 1930 instruction book; 'geometrical apparatus'.

The manual ascribes the mechanism to M. Pierre Th. Dufour who, it is stated, designed this as part of his thesis work for Doctor at the University of Paris. It is also explained that that point C will move in a straight line, perpendicular to line through F and E.

This Meccano model first appears in 1918, so Monsieur Dufour's thesis will likely have been around 1917 (indeed it probably was).

The illustration still shows the long 3/4" version of the double-angle brackets part nr. 11 that was updated in 1917 by the half-inch version. The illustration is made from a photographed model that was thus likely made in the model room in 1917 or perhaps early 1918.

Now reproduced in nickel Meccano also using long, pre-1918 double-angle brackets:

Some minor modifications were made to the illustrated model. A few hinge-points were changed to use round pins instead of screws - these give less play. The mechanism does work, but Meccano still has noticable play on the joints; so point C has a few mm leeway from the straight. It does work, but is more of a straight-ish line mechanism perhaps.

This straight-line mechanism is known as the Peaucellier mechanism of 1864, rather than the Dufour mechanism of 1917. For example, it is shown here in the chapter on straight-line mechanisms in the book 'Ingenious Mechanisms for Designers and Inventors':

It is also known as the Peaucellier-Lipkin linkage or the Peaucellier Inversor.

The Meccano model is indeed the Peaucellier linkage, showing the same point having the linear motion. One difference however is the extra linkages GHK of the Meccano model which seem entirely unneccesary. These links play no role at all in the straight motion, as was already noted in a description of this model in number 39 of the Meccanoman's Journal of July 1975:

This does raise a question; why would Meccano Ltd. in 1918 show this mechanism as a design of M. Dufour and why the extra superfluous linkages? 

Reflecting on the alleged creator; it would be highly unlikely for M. Dufour or the Faculty of Science in Paris to not be aware of the Peaucellier mechanism. It is much more likely that M. Dufour simply used the mechanism as part of his work. Considering this, it is then possible that Meccano Ltd. enthusastically created this model, unawares of it being a Peaucellier Inversor. It is also very much possible that M. Dufour expanded on the Peaucellier Inversor - that would perhaps account for the linkages GHK.

Toying a bit with the mechanism (it really is fascinating); could it be that M. Dufour expanded the mechanism with a point H? It (almost?) makes a straight-line motion parallel with C. Or perhaps its deflection from line EF is of interest, relative to the deflection of point C? And that in writing the description, Meccano did not realise and/or omitted the addition that M. Dufour made to the Peaucellier linkage?

Astonishingly, today it is possible to identify the proibable thesis that this mechanism was created for. Monsieur Pierre Th. Dufour most probably was a Swiss student, who after studying in Lausanne obtained a degree at the Paris University's Faculty of Science in June 1917. His thesis is stored in several university libraries - its content has however not (yet) been digitized. Al least, a digitized version could not readily be found.

(If deeply curious, a copy is available online from an antique books seller.)

Its title "Les perspectives-reliefs : nouveau procédé permettant de les obtenir par simple transposition automatique en projection oblique des formes du terrain représentées sur les cartes hypsométriques" does however give clues what it is about. It is about methods to apply transformations from oblique projections to obtain depth/altitude maps in geography (hypsometry). Linkages seem a logical tool to use for such an undertaking.

Pierre Dufour probably used Meccano to prototype various mechanisms. Maybe he corresponded with Meccano (France?) on the subject, or his work was picked-up on by Meccano.

Ergo - the model as described in the Meccano instructions is actually the Peaucellier mechanism. M. Dufour is likely to have made modifications to obtain specific properties. The superfluous linkages shown, but not described, in the Meccano instructions may be such a Dufour-modification, but its meaning for now unclear.

Perhaps after reading his full thesis the meaning of linkage GHK would become clear. 

Until then - it is anyhow an intriguing mechanism (and remains a bit of a puzzle mystery :)