Linkages

LINKAGES, in mechanics, are an assemblage of rods hinged together so that the parts may move among themselves, being generally intended to perform some particular kind of useful motion. Nearly all machinery consists of linkages either obvious or disguised. The piston rod, crank and connecting rod of a steam engine is a linkage. A pantograph is another. Linkage is used also in biology, to denote the coupling of two hereditary characters (see HEREDITY).

A linkage may consist of any number of rods, arid their motion may take place in a space of three dimensions or in one of two dimensions (a plane). A crank shaft out of alinement would still work, provided the joints permitted it, and would be working in three dimensions. It is, however, only plane linkages which have received much notice, and of them the most attention has been paid to the one which con sists of four rods jointed together to form a deformable quadrilat eral. Considering one bar as fixed, it can be removed and replaced by fixed pivots about which the bars that were jointed to it can rotate. This has caused the mechanism to receive the name "three bar linkage." Watt's Parallel Motion.—The subject of three bar motion appears to have originated in 1784 with the invention by James Watt of his so-called "parallel motion." Writing to his partner, Bolton, in June of that year, he says: "I have started a new hare. I have got a glimpse of a method of causing a piston rod to move up and down perpendicularly by only fixing it to a piece of iron upon the beam without chains or perpendicular guides or untowardly frictions, arch heads or other pieces of clumsiness. I think it a very probable thing to succeed and one of the most ingenious simple pieces of mechanism I have contrived." A visit to the science museum at South Kensington will show the sort of "clumsinesses" which Watt's invention superseded. It was essen tially three bar motion, ACDE (fig. r), the links of which were so adjusted in length and disposition as to cause a point F on the traversing link CD to describe a figure of 8. The portion of the curve near the point of inflexion is nearly straight for an appreciable length. If the two links AC and DE which rotate about the fixed points A and E are of equal length and the point F is in the middle of CD, the figure of 8 is symmetrical ; but if they are of unequal lengths, one limb of the curve is straighter than the other and is straightest when the point F is taken so that CF:FD as DE: AC. If the head of the piston rod were

fixed at F it is clear that the point E would be at an inconvenient distance from the rest of the engine ; so Watt added two more links, BG and DG, forming a parallelogram, and it will be seen that ACDGB forms a pantograph in which the usual tracing point and fixed centre have changed places; and now if AC: CB as CF:FD, the point G will describe a curve similar to that described by F. The head of the piston rod was attached to G.

Peaucellier

Cell.—Several attempts were made in the early part of the 19th century to improve upon Watt's parallel motion, among which we may mention those of Scott Russell and Kaul bach. The "Grasshopper" engine (now shown in the science museum at South Kensington) was one of them. But it was re served to Peaucellier, a lieutenant in the French army, to invent the first exact parallel motion. In 1864 he produced his famous Peaucellier cell, consisting of six links, which converts rotatory motion into a truly straight line. It seems, however, to have completely escaped no tice. Prof. Tchebichoff of the University of St. Petersburg (Leningrad) had been very interested in parallel motion without hav ing arrived at any solution. But a pupil of his, named Lipkin, rediscovered the Peau cellier cell. The invention was introduced into England where it caused great admiration and interest, forming the subject of an ad dress by Prof. Sylvester at the Royal Institution in 1874 (Col lected Works, vol. iii.). It consists of four equal bars, FL, LM, MH, HF, and two other longer equal bars KH and KL, jointed together as shown in fig. 2. The outstanding property of this simple mechanism is that during its deformation KF•KM remains constant ; so that if K is fixed, the curves traced out by F and M are inverse curves. If F describes a circle, M will describe the in verse circle: but if the centre of the F circle is at a distance from K equal to its radius, then the radius of the M circle becomes in finite; i.e., M describes a straight line. This form of parallel mo tion is stated to have been used in an engine installed for the purpose of ventilating the Houses of Parliament before the intro duction of electric fans.