### Gear Trains with Simple Gear Train

**Introduction**:

Sometimes, two or more gears are made to mesh with each other to transmit powerÂ from one shaft to another. Such a combination is called gear train or train of toothedÂ wheels. The nature of the train used depends upon the velocity ratio required and theÂ relative position of the axes of shafts. A gear train may consist of spur, bevel or spiralÂ gears.

**Types of Gear Trains**:

Following are the different types of gear trains, depending upon the arrangement ofÂ wheels:

1. Simple gear train,

2. Compound gear train,

3. Reverted gear train, and

4. Epicyclic gear train.

In the first three types of gear trains, the axes of the shafts over which the gears areÂ mounted are fixed relative to each other. But in case of epicyclic gear trains, the axesÂ of the shafts on which the gears are mounted may move relative to a fixed axis.

**Simple Gear Train**:

When there is only one gear on each shaft, as shown in Fig. 13.1, it is known asÂ simple gear train. The gears are represented by their pitch circles. When the distanceÂ between the two shafts is small, the two gears 1 and 2 are made to mesh with eachÂ other to transmit motion from one shaft to the other, as shown in Fig. 13.1 (a). SinceÂ the gear 1 drives the gear 2, therefore gear 1 is called the driver and the gear 2 isÂ called the driven or follower. It may be noted that the motion of the driven gear isÂ opposite to the motion of driving gear.

Let N1 = Speed of gear 1(or driver) in r.p.m.,

N2 = Speed of gear 2 (or driven or follower) in r.p.m.,

T1 = Number of teeth on gear 1, and

T2 = Number of teeth on gear 2.

Since the speed ratio (or velocity ratio) of gear train is the ratio of the speed of theÂ driver to the speed of the driven or follower and ratio of speeds of any pair of gears inÂ mesh is the inverse of their number of teeth, therefore

It may be noted that ratio of the speed of the driven or follower to the speed of theÂ driver is known as train value of the gear train. Mathematically,

From above, we see that the train value is the reciprocal of speed ratio.Â Sometimes, the distance between the two gears is large. The motion from one gearÂ 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.

Â A little consideration will show that the former method (i.e. providing large sizedÂ gears) is very inconvenient and uneconomical method ; whereas the latter method (i.e.Â 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 ofÂ both the gears (i.e. driver and driven or follower) is like as shown in Fig. 13.1 (b).Â But if the number of intermediate gears are even, the motion of the driven orÂ 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.1(b)

Let N1 = Speed of driver in r.p.m.,

N2 = Speed of intermediate gear in r.p.m.,

N3 = Speed of driven or follower in r.p.m.,

T1 = Number of teeth on driver,

T2 = Number of teeth on intermediate gear, and

T3 = Number of teeth on driven or follower.

Since the driving gear 1 is in mesh with the intermediate gear 2, therefore speedÂ ratio for these two gears is

Similarly, as the intermediate gear 2 is in mesh with the driven gear 3, thereforeÂ speed ratio for these two gears is

The speed ratio of the gear train as shown in Fig. 13.1 (b) is obtained byÂ multiplying the equations (i) and (ii).

Similarly, it can be proved that the above equation holds good even if there are anyÂ number of intermediate gears. From above, we see that the speed ratio and the trainÂ value, in a simple train of gears, is independent of the size and number of intermediateÂ gears. These intermediate gears are called idle gears, as they do not affect the speedÂ ratio or train value of the system. The idle gears are used for the following twoÂ purposes:

1. To connect gears where a large center distance is required, and

2. To obtain the desired direction of motion of the driven gear (i.e. clockwise orÂ anticlockwise).

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