Straight Line Link Mechanisms |
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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. |
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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 (Fig.2), the point C travels in an approximately straight
path. |
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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. |
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A
mechanism whereby the circular motion of the point A is converted
into the accurately rectilinear motion of the point B is illustrated
in Fig.3. In the straight-line link mechanism devised by Watt
(Fig.4a), the point S travels along a so-called lemniscoidal
curve, two parts of which are close approximations of straight
lines. Fig.4b 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. |
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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 (Fig.5) whereby the length of travel of a motion
can be increased or reduced as required. |
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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, as in Fig.7, where this principle is utilized
in the cam lever (or rolling contact lever). |
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