Gear Trains, Ratio, Torque & Direction

For any pair of meshing gears the ratio is the number of teeth on the driven gear divided by the number on the driver. A ratio greater than one is a reduction: the output turns more slowly than the input but delivers proportionally more torque. Ignoring friction, power is conserved, so whatever is gained in torque is lost in speed. Meshing gears also always turn in opposite directions.

An idler gear sits between the driver and the driven gear. Because its teeth cancel in the calculation, appearing once as a driven gear and once as a driver, it has no effect on the overall ratio. Its purpose is to reverse the direction of the output, or simply to bridge a gap between two shafts that are too far apart to mesh directly. This is a favourite examination question: adding an idler changes direction only.

A compound train has two gears fixed on a common intermediate shaft, so they must turn together at the same speed. The overall ratio is then the product of the individual ratios, which allows a large reduction in a compact space, exactly what a helicopter main gearbox or an engine accessory drive needs.

• Try this: Set a simple train with 12 and 36 teeth. Confirm the ratio, then switch to the idler train without changing A or B. Why is the ratio unchanged but the direction reversed?
• Try this: In compound mode, work out the overall ratio by hand from the two stages, then check it against the readout.
• Try this: Increase the reduction and watch the output torque. Where does the extra torque come from, given the input has not changed?