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Updated on February 3, 2010

Linkage, in mechanical engineering, is a system of links, or rigid rods connected by movable joints. The links are joined so that the motion of an input link determines the motion of an output link. Advantage can then be taken of the output motion, either directly or by connecting another machine part to the output link. By varying the proportions of the links and by combining simple linkages into compound linkages, an infinite number of output motions can be obtained for mechanical engineering purposes.

Basic Links

The input and output motions most commonly involved in linkages are rotation, oscillation, and reciprocation- a back-and-forth motion. The basic links for achieving these motions are cranks, levers, and sliders. They may take many forms in different machines, but their effective action is the same.

A crank rotates about a fixed center. A lever oscillates through an angle, reversing its direction of motion at prescribed intervals. A slider moves with a reciprocating motion over the surface of another link in a straight or curved line. These links are connected to each other by rigid parts, termed joints.

Linkage Analysis

In analyzing linkages, it is customary to designate one of the links as the fixed link. The fixed link has no motion relative to the frame of the linkage, although the frame itself may move with respect to another machine part. Generally, in linkage analysis the earth is considered to have no motion, so that a link fixed to the ground is called a fixed, or ground, link. A link that is stationary relative to a moving frame such as an engine in a car is also termed a fixed link.

When linkages are diagramed for the purpose of analysis, it is customary to disregard the thickness or shape of the links perpendicular to the plane of motion. Thus the links are simply represented by lines, whatever the shape of the actual machine part in question may be. Such diagrams (called kinematic, skeleton, or line diagrams) are used to evaluate such characteristics of the linkage parts as velocity, acceleration, and jerk, as well as the paths of motion followed by points on any link.

Quadric Linkage

A four-bar quadric linkage is the simplest kind of linkage, since a closed system of three linked units would essentially be a triangle and therefore a rigid structure. Quadric and other four-bar linkages are classified as simple, while linkages composed of more than four links or of a combination of linkages are classified as compound.

A quadric linkage is composed of a fixed link, a driving link, a driven link, and a connecting link, or coupler, between the driving and driven links. With suitable proportioning and a correct choice of the relative positions of the links a quadric linkage may be used to provide an almost infinite variety of motions between the driving and the driven links. If this basic linkage is modified by making another link the fixed one, the linkages are said to be inversions of each other. An inversion usually changes both input and output motions, but it does not change the relative motion of the links.

If a four-bar linkage is modified so that the alternate links are of equal length, the result is a parallel-motion linkage. Parallel rulers used by draftsmen employ this principle, and the side rod of a steam locomotive is another example.

Slider-Crank Linkage

In its simplest form, the slider-crank linkage consists of a fixed link, a driving crank, a driven slider, and a link connecting the crank and the slider. This form of linkage is used to change a rotary input motion into a straight-line, or curved, reciprocating output motion, or the reverse. The slider-crank linkage is a line or diagrammatic representation of a compressor, pump, or automobile engine.  Often it is desirable to invert and combine the quadric and slider-crank linkages.

Spatial Linkages

Thus far only plane-motion linkages have been considered, in which all the points on the links making up the linkage move in the same or parallel planes.

Spatial linkages, on the other hand, provide six degrees of freedom of motion - three of translation and three of rotation - and are not easily represented and visualized. Such linkages have been in specialized use for many years, but are only now being analyzed and synthesized by kinematicians. The universal joint commonly-used in automotive transmissions, and known as the Hooke or Cardan joint, is probably one of the best known of these linkages.

Other Linkages

Although a limitless number of motions can be generated with linkages, only a few others will be mentioned here. The quick-return mechanism, used in various machine tools, is a combination of quadric and slider-crank linkages. By changing the relative dimensions of the linkage, the tracing can be made as an enlargement or a reduction.

Many linkages developed at the beginning of the Industrial Revolution were devised to provide a straight-line movement. The Scottish engineer James Watt devised an approximate straightline mechanism in order to make possible a double-acting steam engine, in which work was done both by the downstroke and by the return stroke of the single piston. Various linkages have since been devised that provide a true straight-line movement.


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