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1. ## Peaucellier-Lipkin linkage - GIF

Peaucellier-Lipkin linkage, the first planar linkage capable of transforming rotary motion into perfect straight-line motion.

Previously:

Rolling Ball Sculpture and Linkage Simulator
Shaft linkage design for oppositely-rotating shafts - GIF
Lever advancing ratchet mechanism - GIF
Linear oscillating to rotational motion gear design - GIF
Conjugate cams animation - GIF

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3. OK, I think it is quite an elegant bit of mechanical art. Now I have to ask where you would use it?

4. Probably some engineer with a govt. grant to play with.

Probably some engineer with a govt. grant to play with.
Probably not likely, it was invented in the 1860's. As for applications, a bit of info here (as much as I hate to quote wikipedia):

"Until this invention, no planar method existed of converting exact straight-line motion to circular motion, without reference guideways. In 1864, all power came from steam engines, which had a piston moving in a straight-line up and down a cylinder. This piston needed to keep a good seal with the cylinder in order to retain the driving medium, and not lose energy efficiency due to leaks. The piston does this by remaining perpendicular to the axis of the cylinder, retaining its straight-line motion. Converting the straight-line motion of the piston into circular motion was of critical importance. Most, if not all, applications of these steam engines, were rotary.

The mathematics of the Peaucellier–Lipkin linkage is directly related to the inversion of a circle."

Most of these linkages were (I expect still are) developed as mathematical problems to be worked on and solved either to solve some particular real world problem or just for the sake of understanding the minute details of the world more deeply. Eventually lots of them trickle down into real world use. I don't pretend to understand much of the esoteric analysis behind stuff like this but find it all fascinating nonetheless. I have read a few books on the study of linkages and while I feel like I can follow much of what is being explained, the understanding leaves me pretty soon after I read it.

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7. The linkage was typically used with early beam engines before the development of crossheads that would allow the piston connecting rod to always move linearly while directly driving the crankshaft.

The photo shows the vertically oriented cylinder driving the end of the beam (which moves in an arc) via a Peaucellier linkage. The other end of the beam then drives a rotary power takeoff shaft via a conventional crank.

These engines were operated at low speeds and the linkage helped extend their useful life to many decades at the expense of complexity and increased frictional losses.

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9. Originally Posted by clavius
Probably not likely, it was invented in the 1860's. As for applications, a bit of info here (as much as I hate to quote wikipedia):

"Until this invention, no planar method existed of converting exact straight-line motion to circular motion, without reference guideways. In 1864, all power came from steam engines, which had a piston moving in a straight-line up and down a cylinder. This piston needed to keep a good seal with the cylinder in order to retain the driving medium, and not lose energy efficiency due to leaks. The piston does this by remaining perpendicular to the axis of the cylinder, retaining its straight-line motion. Converting the straight-line motion of the piston into circular motion was of critical importance. Most, if not all, applications of these steam engines, were rotary.

The mathematics of the Peaucellier–Lipkin linkage is directly related to the inversion of a circle."

Most of these linkages were (I expect still are) developed as mathematical problems to be worked on and solved either to solve some particular real world problem or just for the sake of understanding the minute details of the world more deeply. Eventually lots of them trickle down into real world use. I don't pretend to understand much of the esoteric analysis behind stuff like this but find it all fascinating nonetheless. I have read a few books on the study of linkages and while I feel like I can follow much of what is being explained, the understanding leaves me pretty soon after I read it.

I'm not disagreeing with you but there's a much simpler way to do it. Think of a steam locomotive. If you spin the drive wheel the piston rod will make a nice linear move.

10. It looks more like they're transferring a linear motion (no matter how it's achieved) to a perpendicular linear motion. The method here seems to start with an eccentric wheel trapped between two blocks (not exactly a locomotive motion?) to create the horizontal motion then the linkages that follow to create the vertical linear motion. Or am I missing something? The "wheel" actuation is pretty typical, so nothing new there, it's the following pantograph type linkages, with two fixed points running off of a gear and rack, that transfer the first horizontal linear motion to the perpendicular linear motion. This apparently 3d printed version has a lot of play in it that an actual application would not allow.

11. Originally Posted by Hoosiersmoker
It looks more like they're transferring a linear motion (no matter how it's achieved) to a perpendicular linear motion. The method here seems to start with an eccentric wheel trapped between two blocks (not exactly a locomotive motion?) to create the horizontal motion then the linkages that follow to create the vertical linear motion. Or am I missing something? The "wheel" actuation is pretty typical, so nothing new there, it's the following pantograph type linkages, with two fixed points running off of a gear and rack, that transfer the first horizontal linear motion to the perpendicular linear motion. This apparently 3d printed version has a lot of play in it that an actual application would not allow.
I'm guessing you didn't understand my point. If you want to design something that does a simple thing into something complicated then, Bob's your uncle, there it is. My point was it could be simpler. Also the locomotive idea with an added linkage at the end of the "cylinder rod" sort of L shaped turned cw 90 degrees with a swivel point at the convergence of the two straight parts of the L and another rod at the other end of the L would produce motion up and down, if that is what apparently is vitally important. There are many ways it could be done.

I'm not disagreeing with you but there's a much simpler way to do it. Think of a steam locomotive. If you spin the drive wheel the piston rod will make a nice linear move.
Yes the piston rod moves linearly. However, it drives a slider in the crosshead which also moves linearly. The link driving the rotating wheels connects to the slider, not the piston rod. The forces perpendicular to the motion of the piston are absorbed by the slider pushing against the crosshead. There is essentially no perpendicular force on the piston rod.

It was the invention of the crosshead that allowed the piston to drive the crankshaft/loco wheel directly that eliminated the need for the overhead beam and the various linkages, Peaucellier included.

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I'm not disagreeing with you but there's a much simpler way to do it. Think of a steam locomotive. If you spin the drive wheel the piston rod will make a nice linear move.
I do get what you are saying. I think the point in this instance is what is noted in the description: "converting exact straight-line motion to circular motion,without reference guideways.

I think it's the lack of reference guideways that was the important point of this particular linkage, for an application like the beam engine that Marv K. posted.

To your point, there is are much simpler ways to do this, but until crossheads came along this was one workable (if more complex) way to accomplish that conversion.

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