The Peaucellier Linkage

The Peaucellier Linkage

 

I’m a nerd, so I think this mechanism is really cool.  When I was a kid, I asked myself if there were some planar linkages that could generate a straight line.  I occasionally brainstormed on this for many years, without success.

After a long time (but before search engines were widely available) I inherited my father-in-law’s library and I found this:

It has the solution:  The “Peaucellier Linkage”.  It also describes some of the history behind straight-line linkages, and I feel slightly vindicated.  In the early days of steam engines, Engineers needed a straight-line linkage, and some powerful mathematicians (no less than Chebyshev himself) tried to solve this problem exactly but without success.  So I’m not smarter than Chebyshev; I can live with that.  It wasn’t until some time later that some smart-aleck Captain in the French Army showed them up: Charles-Nicolas Peaucellier.

The above video shows how it works, and it shows what is needed to make it work.  The exact dimensions don’t matter, as long as the congruent links are the same length.

There is a good article on Wikipedia describing the mathematics behind it.

And, yes, that’s Lego Technics.

Okay, I warned you not to read this if you are not a nerd, so no complaints about how this is SOOOO boring, please.  Although I always welcome discussions and challenges to my opinions.

P.S.  Can anybody tell me how to pronounce “Peaucellier”?