Бұрылыс қозғалысын түзу сызықты қозғалысқа айналдыратын механизм

Mechanical linkage capable of transforming rotary motion into linear motion

The Peaucellier–Lipkin linkage (or Peaucellier–Lipkin cell, or Peaucellier–Lipkin inversor), invented in 1864, was the first true planar straight line mechanism – the first planar linkage capable of transforming rotary motion into perfect straight line motion, and vice versa. It is named after Charles Nicolas Peaucellier (1832–1913), a French army officer, and Yom Tov Lipman Lipkin (1846–1876), a Lithuanian Jew and son of the famed Rabbi Israel Salanter. 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.

There is an earlier straight line mechanism, whose history is not well known, called the Sarrus linkage. This linkage predates the Peaucellier–Lipkin linkage by 11 years and consists of a series of hinged rectangular plates, two of which remain parallel but can be moved normally to each other. Sarrus' linkage is of a three dimensional class sometimes known as a space crank, unlike the Peaucellier–Lipkin linkage which is a planar mechanism.

In the geometric diagram of the apparatus, six bars of fixed length can be seen: , , , , , The length of is equal to the length of , and the lengths of , , , and are all equal forming a rhombus. Also, point O is fixed. Then, if point B is constrained to move along a circle (for example, by attaching it to a bar with a length half way between O and B; path shown in red) which passes through O, then point D will necessarily have to move along a straight line (shown in blue). In contrast, if point B were constrained to move along a line (not passing through O), then point D would necessarily have to move along a circle (passing through O).

Thus, by the properties of inversive geometry, since the figure traced by point D is the inverse of the figure traced by point B, if B traces a circle passing through the center of inversion O, then D is constrained to trace a straight line. But if B traces a straight line not passing through O, then D must trace an arc of a circle passing through O. Q. E. D.

Peaucellier–Lipkin linkages (PLLs) may have several inversions. A typical example is shown in the opposite figure, in which a rocker slider four bar serves as the input driver. To be precise, the slider acts as the input, which in turn drives the right grounded link of the PLL, thus driving the entire PLL.

Sylvester (Collected Works, Vol. 3, Paper 2) writes that when he showed a model to Kelvin, he “nursed it as if it had been his own child, and when a motion was made to relieve him of it, replied ‘No! I have not had nearly enough of it—it is the most beautiful thing I have ever seen in my life.’”

A monumental scale sculpture implementing the linkage in illuminated struts is on permanent exhibition in Eindhoven, Netherlands. The artwork measures , weighs , and can be operated from a control panel accessible to the general public.