Sorting mechanism

Consider a kind of lambda mech­a­nism that trans­lates the uniform motion of a gray hinge around a circle into the motion of a blue hinge along some curve.

The para­me­ters of the mech­a­nism are chosen so that part of the trajec­tory of the blue hinge is close to the arc of some circle. The move­ment along this part of the trajec­tory takes more than half of the time.

Let's add another link to the mech­a­nism: ”the radius.” As the blue hinge moves along a segment of a trajec­tory close to a circle, the free end of the new link will oscil­late about the center of that circle.

If the free end of ”the radius” controls the motion of another link, the yoke, it will remain stationary most of the time (in layman's terms, geomet­ri­cally there will be small devi­a­tions), and then make a rapid full roll back and forth. As they say in mechanics, it's a mech­a­nism with a long stop of the slave link at the end of its stroke.

This beau­tiful geometric idea was devised by the greatest Russian math­e­mati­cian Pafnuty L. Tcheby­shev to create an elegant mech­a­nism, designed for the impor­tant prac­tical task of sorting grain. Both in the 19th century and today, grain is sorted by weight in order to select the best - heavier - grains.

The grain was poured into a box. It has not survived and has been recon­structed from a photo­graph. Next, through a curved channel, the grain entered a tray attached to the end of the link, which had a long stop. Since the arm stop lasts more than half the time, during this interval the grain fills the tray. Rapid rolling back and forth will scatter the grain. To prevent the grain from spilling out of the box at the moment of rolling, to the kine­matic scheme consid­ered at the begin­ning of the film. The kine­matic scheme in the mech­a­nism is supple­mented by another chain. ”A pickup,” attached to one of the links, blocks the exit from the box at the moment of rolling.

The sharp ejec­tion from the tray sorts the grains by weight. The best — heavier — grains end up (on average) lying further away from the mech­a­nism.

The bulk of the sorting machine is kept in the Museum of the History of St. Peters­burg Univer­sity, as is the photo of the univer­sity's mechan­ical cabinet (taken by B. N. Menshutkin in the end of the 19th century). Based on these sources, this video presents a working exact replica of the mech­a­nism.

Other etudes in “Tchebyshev's Mechanisms”