# Idler Gear – Purpose, Torque Calculation, Reverse Application

#### Equipment

An idler gear, as the name implies, does no work. However, its use is frequent in drive trains where its default position is between a driving gear and a driven counterpart. In this article, you will learn about the purpose of the idler gear, its influence in torque calculations, as well as review the reverse idler gear.

## Purpose of Idler Gears

Although idler gears do not perform work, they have two basic functions that make them popular in transmission systems. One is to change the direction of rotation, while the other is to enable transmission over a long distance.

### Direction of Rotation

Whenever two gears mate, they rotate in the opposite direction. Moreover, in some applications, this could be problematic as the wish is to transmit only torque without a change in the rotation direction. Thus, the use of an idler gear between the driving and the driven gears.

Following the figure above, as the driver gear rotates anticlockwise, the idler gear rotates clockwise because they both mate. In turn, the driven gear rotates in the anticlockwise direction, opposite to the direction of the idler gear. As a result, the initial direction of rotation is maintained in gear trains by using idlers.

### Transmission Over a Long Distance

When there is a significant distance between the centerline of shafts, flexible drives such as belts and chains are often the choice of designers for power transmission. But these drives come with a host of challenges. For example, belt drives often experience slip and creep, which reduces the efficiency of transmission. Chain drives invite limitations in load capacity, and precision of motion, and only work if shafts are parallel. So, to overcome these limitations, gear trains can be used with idler gears in the configuration. Importantly, this helps minimize the physical size of the interconnecting gears.

## Torque Calculations

When reviewing the torque relationship in a gearing system, it is important to consider the law of gearing. Moreover, this law states that the angular velocity of all gears in the mesh must remain constant. As a result, the following relationship for gear speed and torque calculations apply:

In the relation above, ω1 and ω2 represent the angular velocities for the driver and driven gears respectively. n1 and n2, d1 and d2, and T1 and T2 represent the number of teeth, diameter, and torque of the driver and driven gears respectively. Generally, it is common to refer to this relation as the gear ratio, and it serves as the governing expression for calculating gear train parameters. Using this expression, the speed and torque ratio of a gear train with an idler gear is analyzed as follows:

From the speed and torque relations above, the resultant ratio is always a function of the driver and driven values. So, despite the number of idler gears in a gear drive, their impact is always cancelled out. Thus, this expression from the gear law proves mathematically that idler gears do not influence the speed and torque of a gear train.

## The Reverse Idler Gear

Reverse idler gears serve to change the direction of rotation when transmitting torque between two shafts. They have several applications but are most popular in a manual vehicle transmission.

In these manual systems, the driver moves the gear selector for the clutch to engage the desired gear ratio. Because the gears on the layshaft directly engage those on the output shaft, the direction of rotation of the output shaft is opposite to that of the layshaft. Thus, it moves the car forward.

However, an idler gear is positioned between both shafts at the reverse gear location, which is at the extreme right in the figure above. As a result, the direction of rotation changes and causes the output shaft to rotate in the same direction as the layshaft when this gear ratio is in play. Hence the car moves backwards. Using an idler gear in this setup ensures that the same output shaft serves in propelling the vehicle either forward or backwards.