What condition must hold true for two gears to mesh properly in an automotive gearbox?

For two gears to mesh properly in an automotive gearbox, it is essential that the teeth are of compatible sizes. This is because the size and shape of the teeth determine how well they can interlock and transfer motion and power between the gears. If the teeth are not the same size, they will not fit together properly, which can lead to inefficient operation, increased wear and tear, or even mechanical failure.

In a gearbox, gears are designed with specific parameters, including the pitch (the distance between corresponding points on adjacent teeth), profile, and diameter. When these parameters do not align correctly, the gears cannot effectively engage with each other, resulting in poor performance and potential damage to the gearbox system. Therefore, ensuring that the teeth of both gears are of the same size is crucial for their proper functionality and longevity within the automotive gearbox.