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Unformatted text preview: ar 2 (or driven or follower) in r.p.m.,
T 1 = Number of teeth on gear 1, and
T 2 = Number of teeth on gear 2. Since the speed ratio (or velocity ratio) of gear train is the ratio of the speed of the driver to
the speed of the driven or follower and ratio of speeds of any pair of gears in mesh is the inverse of
their number of teeth, therefore
Speed ratio = N1 T2
=
N 2 T1 It may be noted that ratio of the speed of the driven or follower to the speed of the driver is
known as train value of the gear train. Mathematically,
Train value = N 2 T1
=
N1 T2 From above, we see that the train value is the reciprocal of speed ratio.
Sometimes, the distance between the two gears is large. The motion from one gear to another,
in such a case, may be transmitted by either of the following two methods :
1. By providing the large sized gear, or 2. By providing one or more intermediate gears.
A little consideration will show that the former method (i.e. providing large sized gears) is
very inconvenient and uneconomical method ; whereas the latter method (i.e. providing one or more
intermediate gear) is very convenient and economical.
It may be noted that when the number of intermediate gears are odd, the motion of both the
gears (i.e. driver and driven or follower) is like as shown in Fig. 13.1 (b).
But if the number of intermediate gears are even, the motion of the driven or follower will be
in the opposite direction of the driver as shown in Fig. 13.1 (c).
Now consider a simple train of gears with one intermediate gear as shown in Fig. 13.1 (b).
Let N 1 = Speed of driver in r.p.m.,
N 2 = Speed of intermediate gear in r.p.m., 430 l Theory of Machines
N 3 = Speed of driven or follower in r.p.m.,
T 1 = Number of teeth on driver, T 2 = Number of teeth on intermediate gear, and
T 3 = Number of teeth on driven or follower.
Since the driving gear 1 is in mesh with the intermediate gear 2, therefore speed ratio for
these two gears is N1
T
=2
N2
T1 ...(i) Similarly, as the intermediate gear 2 is in mesh with the driven gear 3, therefore speed ratio
for these two gears is T
N2
...(ii)
=3
N3
T2
The speed ratio of th...
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This note was uploaded on 02/13/2014 for the course MIE 301 taught by Professor Celghorn during the Fall '08 term at University of Toronto.
 Fall '08
 CELGHORN

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