Linkwork


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Linkwork

 

(in Russian, sharnirnyi mekhanizm), a mechanism whose elements (links) form only rotating kinematic pairs (linkages).

Depending on the type of motion of the links, linkworks are classified as plane, spherical, and general three-dimensional. In plane linkworks the axes of the linkages are parallel, and all links therefore undergo plane-parallel motion. The simplest plane linkwork consists of four links and is called a four-bar linkage. In spherical linkworks the axes of the linkages intersect at a single point. The smallest number of links in a spherical linkwork also is four. A spherical four-link motion (Figure 1) is used, for example, in multipiston pumps and aircraft stabilizers. The Cardan mechanism is a particular case of the spherical four-bar motion, in which the axes of two rotating pairs are mutually perpendicular. In three-dimensional linkworks the axes of the rotating pairs cross at different angles. In the general case a three-dimensional linkwork should have at least seven links (a three-dimensional seven-bar motion). When certain relations between the linear and angular dimensions of the links are satisfied, however, the minimum number of links is reduced to four (for example, Bennett’s mechanism). Three-dimensional linkworks find application in agricultural machinery and automatic machines used in food processing and light industry.

Figure 1. Spherical four-bar motion: (0) fixed link, (1), (2), and (3) movable links

Depending on the method used to define the required motion of a working link, linkworks are subdivided into positioning, guiding, and transmission mechanisms and mechanisms for interrupted motion. Positioning linkworks are designed to move a working link from one position to another; the number of defined positions is usually two, less often three or four. Such linkworks are used in metallurgical machines (such as tilters, tippers, and mechanisms for plugging tap holes) and in automatic machinery for the food-processing industry (for positioning working members of machines). Guiding linkworks are designed to move along a specified curve a single point of a link that does not form a kinematic pair with the stay. Linkworks that guide along the arc of a circle (circular guiding mechanisms) and straight-line mechanisms, such as the Chebyshev parallel motion, are the most widely used types. Linkworks are also used to shape parabolas and hyperbolas, such as the mechanisms for grinding the mirrors

Figure 2. Linkwork for interrupted motion

of astronomical instruments. Transmission linkworks are designed to convert rotary motions according to a specific law. They act as mechanisms for reproducing a given function. In calculators, transmission linkworks are used to perform such mathematical operations as addition, multiplication, and raising to powers. Through special selection of the lengths of the links, it is possible to obtain an approximate reproduction of diverse functions. For example, when the function y = f (x) is reproduced, the angles of rotation of one rotating link are proportional to the argument x, and the angles of rotation of the other are proportional to the function y.

Linkworks for interrupted motion are used in automatic machines to set in motion a working member that, after completing a specific operation, must remain stationary for some period of time while the other working members move. A diagram of a six-bar linkwork for interrupted motion is shown in Figure 2. The mechanism transforms the continuous motion of link AB into the motion of link EF with prolonged stops in a single position. The linkwork is based on the circular guiding mechanism A BCD, in which the lengths of the links are selected such that the trajectory of point M on the section marked by the heavy line on the diagram nearly coincides with the arc of a circle of radius R. As point M moves along the segment, link EF remains stationary if the length of link EM is equal to radius R and point E coincides with the center of the circle at this time. As point M moves along a different segment of the trajectory, link EF is shifted by some angle and returns to the stop position.

Linkworks are widely used in various fields of engineering because of their simplicity of manufacture and high reliability. Their shortcomings include relatively large size and the possible appearance of significant forces acting on the links at positions where the displacement of some center of a linkage subtends an angle close to 90° with the effective force. Furthermore, not all laws that may be required for the transformation of motion can be obtained by means of linkworks.

REFERENCES

See references under MECHANISM.

N. I. LEVITSKII