4 Bar Linkage
(old)
In all applications of 4-bar linkages one bar is fixed and is termed the
frame; see AB in the figure above. The two bars which rotate about the fixed
points A and B are termed cranks, while the bar DC opposite the frame is called
the coupler.
The characteristics of a given 4-bar linkages clearly depend on the
relative lengths a, b, c, d of the bars and which bar is chosen as the frame.
For the linkage to exist at all it is clear that no single bar can be longer
than the sum of the remaining three, so:
a < b + c + d
b < a + c + d
c < a + b + d
d < a + b + c
but other relevant inequalities are not so obvious.
(Bolt B., Mathematics meets technology, 2007, pg. 82)
(new/better)
Figure shows an example of 4-bar linkage.
For 4-bar linkage there exist constraints by which the motion of 4-bar linkages
is divided into some types, what we call, double crank, crank-rocker, or
double-rocker mechanism. According to Harding’s notation, the constraints are
experessed as follws:
Class I : a-b< c-d
Class II: a-b>c-d
Where,
a+b > c+d, a>b, c>d
although the constraints exist, they can
not anticipate the motion of the point p, but the motion of the drive and the
folllwing link. For example if a linkage is double crank two links completely
turn aruond their fixed points as the drive link is moved. Therefore is the
motion of the point p could be estimated by the relation of length of links, it
is very useful fort he linkage design.
( H.
Kangassalo,Setsuo Ohsuga, Information Modelling and Knowledge Bases, 8. cilt, p.106)
Ferguson's Paradox
(old)
There is no old definition
(new/better)
the figure shows an epicyclic gear train
known as Ferguson's Paradox. Gear A is fixed to the frame and is, therefore
stationary. The arm B and gears C and D are free to rotate on shaft S. Gears A,
C,D have 100, 101, and 99 teeth respectively, all cut to same pitch circle diameter
from gear blanks of the same diameter so that same planet wheel of 20 teeth
meshes with all of them. Determine the revolutions of gears C and D for one
revolution of teh arm B.
(Ambekar,Ambekar A.g.,Mechanism and Machine
Theory, p.386)
Hook's Coupling (Universal Joint)
(old)
This
joint is used to connect two non-parallel interesting shafts. It is also used
for shafts with angular misalignment where flexible coupling does not serve the
purpose. Thus, Hooke's joint is means of connecting two rotating shafts whose
axes lie in one plane, their directions making a small angle with each other.
(The theory of machines and mechanisms, Emilio Bautista, p.
68)
(new/better)
It is a rigid coupling that connects two
shafts, whose axes intersect if extended. It consists of two forks which are
keyed to the shafts. The two forks are pin joined to a central block, which has
two arms at right angle to each other in the form of a cross. The angle between
shafts may be varied even while the shafts are rotating.
( K. L. Narayana, Machine Drawing, p.123)
Toggle Joint
(old)
A link mechanism commonly known as a toggle joint is applied to machines of different types, such as drawing and embossing presses, stone crushers, etc., for securing great pressure. The principle of the toggle joint is shown by diagrams A and B, in Fig. II.
There are two links, b and c, which are connected
at the center. Link b is free to swivel about a fixed pin or
bearing at d, and link c is connected to a sliding
member e. Rod fjoints links b and c at
the central connection. When force is applied to rod f in a
direction at right angles to centre-line xx, along which the driven
member e moves, this force greatly multiplied at e,
because a movement at the joint g produces a relatively slight
movement at e. As the angle é becomes less, motion
at e degreases and the force increases until the links are in
line, as at B. If R= the resistance at e, P= the applied power or
force, andé= the angle between each link and a line xx through
yhe axes of the pins then: 2R sin é=P cos é.
( Franklin Day Jones, Mechanisms and Mechanical Movements, Elibron
Classics, 2005, p. 18-19)
(new/better)
Front wheel braking efficiency can be
stepped up on fords by a toggle joint arrangement which replaces teh usual
operating wedge and rollers. With half the pedal pressure applied to the
regulation brake, the braking power can be increased 100 percent. The effect is
to put sixty per cent of the braking load on the front wheels of the automobile
and eliminate any tendency of brakes to groan and chatter.
(Popular Mechanics, p. 231)
Worm Gear
(old)
In
worm gears, the axes are non- intersecting and the planes containing the axes
are normally at right angle to each other. Worm- gear is a special case of a
crossed helical gear or spiral gear in which the shaft angle is 90o. The hand
of helix is the same for both mating gears. To get large speed reduction in
skew shafts and to transmit a little higher load than usual spiral gear, use of
worm and worm gears can be made. Worm gears have wide application in hoisting
equipments, due to the itself locking ability.
A single-enveloping worm gear set has a cylindrical worm with a throated gear wrapped around the worm and there is a line contact between the teeth.
A double-enveloping worm gear set has both members throated and wrapped around the worm each other and there is a area contact between the teeth.
The worm gear is normally the driven member of the pair and is amde to envelop (or wrap around) the worm. The axis length of the worm is increased so that at least one or two threads, called as teeth, complete the circle on it.
The worm is a member having the screwlike thread and worm theet are frequently named as threads. Worms in common use have 1 to 8 teeth, and, as well as there is no definite relation between the number of teeth and the pitch diameter of a worm. Worms may be designed with a cylindrical pitch surface as shown in the figure. A worm can be single, double or triple start.
(Theory of Machines and Mechanisms - II, H.G Phakatkar, p.636-637)
A single-enveloping worm gear set has a cylindrical worm with a throated gear wrapped around the worm and there is a line contact between the teeth.
A double-enveloping worm gear set has both members throated and wrapped around the worm each other and there is a area contact between the teeth.
The worm gear is normally the driven member of the pair and is amde to envelop (or wrap around) the worm. The axis length of the worm is increased so that at least one or two threads, called as teeth, complete the circle on it.
The worm is a member having the screwlike thread and worm theet are frequently named as threads. Worms in common use have 1 to 8 teeth, and, as well as there is no definite relation between the number of teeth and the pitch diameter of a worm. Worms may be designed with a cylindrical pitch surface as shown in the figure. A worm can be single, double or triple start.
(Theory of Machines and Mechanisms - II, H.G Phakatkar, p.636-637)
(new/better)
many circumstances arise in which the
speed of a machine’s output gear must be reduced. When hign reduction rates are
required, worm gear setsare often used, singly or in multiples. Calculation of
speed ratios of worm gear stes involves the threading of the worm. A single
thread worm will turn the worm gear the distance of one tooth each time the
worm turns one revolution. The single thread worm is treated as a one-toorh
gear. A double-thread worm moves the gear two teeth per revolution and is
treated as a two-tooth gear. The same idea holds for triple-thread worm gears,
quadruple-thread, and so an.
The familiar Formula for worm gear
calculation is:
(Ww/Wg)= (Ng/Nw)
Wg:
speed of gear
Ww:
speed of worm
Ng:
number of teeth on gear
Nw:Number of threads on worm
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