
In light vehicle applications, the engine operates over a wide speed range, but produces maximum torque only within a relatively narrow RPM band.
A relatively large turning effort must be applied to the driving road wheels to move the vehicle. Then the turning effort must vary, to overcome air and gradient resistance and rolling resistance.
A manual transmission allows the driver to directly vary the gear ratio, between the engine and the driving road wheels. This allows engine torque to be varied, to suit load and speed requirements.
The transmission also provides a means of reversing the vehicle. And it has a neutral position, which disconnects the engine from the driving wheels.
When two gears are in mesh, one is a driven, or “output” gear. The other, providing the turning action, is the driver or “input gear”.
A gear ratio is the number of turns of the input gear, necessary to achieve one turn of the output gear. Here it is 1 to 1 since the gears have the same number of teeth.
In rotation, they also turn at the same speed, and the turning effort of the output gear, will equal the effort applied by the input gear.

The gear ratio can also be calculated, by dividing the number of teeth on the driven gear, by the number of teeth on the driver gear. In this case, the driven gear has 30 teeth and the driver gear has 10. So the ratio is 3 to 1.
The driver gear has to turn three times, to turn the driven gear once. In continuous rotation, the driven gear turns three times slower than the driver.
Lower speed produces higher torque. So torque at the output is higher. For this gear ratio of 3-to-1, if input torque is 100 Newton Meters, then output torque is 3 times that: 300 Newton Meters.
When three gears are in mesh, the input and output gears are meshed with an “idler” or intermediate gear.
The idler transfers movement between the input and output gears, but has no effect on the ratio, or the torque multiplication. These remain unchanged.