Motion in a straight line

It’s easy to get something to move in a circle; just pin one end down and rotate the rest (like the kind of compass you draw with) or pin the center down and rotate (like a merry-go-round). But how do you get something to move in a perfectly straight line, as is needed, for example, in engines with pistons? I’m reading a delightful book from the 1960’s called “The How and Why of Mechanical Movements,” and the subject of straight-line motion came up in chapter 2 (Levers).

It turns out that a clever arrangement of a collection of rigid bars, connected into a linkage, can give you this magical straight-line motion. Various inspired inventors have come up with different ways to achieve it, and their concepts are illuminating and fascinating.

There’s Watt’s linkage, which requires only three links. It doesn’t quite produce perfectly straight motion (note path of the red point in the animation at right), but good enough that it was used by early steam engines. It’s still used in the rear axle suspension of some vehicles, so that no sideways motion is permitted between the body of the car and the axle (the axle only moves in a vertical straight line with respect to the car body).

The Chebyshev linkage (below left) likewise uses three links and achieves a straighter line, within a prescribed range. In 1864, the Peaucellier-Lipkin linkage (below right) was invented, and it even comes with a proof of collinearity. (These animations are awesome!)

The authors of “How Round is Your Circle?” (another book that looks absolutely engrossing) have an excellent supplementary website. One page shows some beautiful physical incarnations of the almost-straight-line linkages as well as the truly straight-line linkages (check out the videos!).

And now, I’m off to read about more fabulous mechanical movements and be awed by others’ ingenuity.