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Straight Line Link Mechanisms
A large variety of link mechanisms, or linkages, enable movements to be produced which are exactly or at least approximately rectilinear “” i.e., directed along a straight line. The operated motion may be circular or rectilinear. A four-bar linkage can be so contrived that certain points of the mechanism describe substantially straight paths.
One such contrivance, proposed by Hoecken, is shown in Fig.1. Particularly favorable dimensions are obtained when the stationary link d is made twice as long as a. In the case of the oscillating crank, the point C travels in an approximately straight path.
In the late seventeenth century, before the development of the milling machine, it was extremely difficult to machine straight, flat surfaces. For this reason, good prismatic pairs without backlash were not easy to make. During that era, much importance was given to the problem of attaining a straight-line motion as a part of the coupler curve of a linkage having only revolute connection. Probably the best-known result of this search is the straight line mechanism developed by Watt for guiding the piston of early steam engines. Although it does not generate an exact straight line, a good approximation is achieved over a considerable distance of travel.
A mechanism whereby the circular motion of the point A is converted into the accurately rectilinear motion of the point B. In the straight-line link mechanism devised by Watt, the point S travels along a so-called lemniscoidal curve, two parts of which are close approximations of straight lines. It shows the mechanism for a particular type of gas-pressure indicator used with a piston-operated machine; the pressure is exerted upon a spring-loaded measuring piston K in a measuring cylinder, so that the piston is raised a greater or lesser amount, depending on the magnitude of the gas pressure.
This motion is so transmitted to the recording stylus S that the latter performs a rectilinear vertical motion and records the pressure as a function of the position of the machine”s working piston, the rotation of the recording drum being synchronized with the movement of this last-mentioned piston. Accurately rectilinear motion can also be obtained by a pantograph-type mechanism. whereby the length of travel of a motion can be increased or reduced as required.
In the cardan gears, which is invented by Cardano illustrated in Fig.6 the inner wheel has half the radius of the outer. Any particular point on the circumference of the inner wheel, as the latter rotates within the outer wheel, moves on a straight line which passes through the center of the outer wheel and through the two points where that circumferential point on the inner wheel comes into contact with the outer wheel in the course of each revolution. Instead of completely circular wheels it is possible to use parts of circles “” i.e., circular arcs, where this principle is utilized in the cam lever (or rolling contact lever).