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Unformatted text preview: a gear A and the arm C have a common axis at O1 about which they can rotate. The
gear B meshes with gear A and has its axis on the arm at O2, about which the gear B can rotate. If the * We know that speed ratio = Speed of first driver N A
Speed of last driven N D NA
= A× C
NA NC ...(N B = NC, being on the same shaft) For N and N to be same, each speed ratio should be 12 so that
= A × C = 12 × 12 = 12
ND Chapter 13 : Gear Trains l 437 arm is fixed, the gear train is simple and gear A can drive gear B
or vice- versa, but if gear A is fixed and the arm is rotated about
the axis of gear A (i.e. O1), then the gear B is forced to rotate
upon and around gear A . Such a motion is called epicyclic and
the gear trains arranged in such a manner that one or more of
their members move upon and around another member are
known as epicyclic gear trains (epi. means upon and cyclic
means around). The epicyclic gear trains may be simple or compound.
The epicyclic gear trains are useful for transmitting
high velocity ratios with gears of moderate size in a comparatively lesser space. The epicyclic gear trains are used in the
back gear of lathe, differential gears of the automobiles, hoists,
pulley blocks, wrist watches etc. Fig. 13.6. Epicyclic gear train. 13.8. Velocity Ratioz of Epicyclic Gear Train
The following two methods may be used for finding out the velocity ratio of an epicyclic
1. Tabular method, and 2. Algebraic method.
These methods are discussed, in detail, as follows :
1. Tabular method. Consider an epicyclic gear train as shown in Fig. 13.6.
Let T A = Number of teeth on gear A , and
T B = Number of teeth on gear B . First of all, let us suppose that
the arm is fixed. Therefore the axes of
both the gears are also fixed relative to
each other. When the gear A makes one
revolution anticlockwise, the gear B will
make *T A / T B revolutions, clockwise.
Assuming the anticlockwise rotation as
positive and clockwise as nega...
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- Fall '08