Match the transmission device to the job
Transmission carries rotary drive from a driver to a driven shaft, often changing speed or direction. Bevel gears carry drive between shafts at about 90 degrees. A worm and wormwheel give a large reduction in one 90-degree step and are non-reversible. A rack and pinion turns rotary into linear motion. A belt and pulley is cheap and slips if overloaded; a chain or toothed belt gives positive, non-slip drive (a camshaft).
Velocity ratio and output speed from teeth
The velocity ratio of a meshing gear pair is driven teeth / driver teeth; a big driven on a small driver gives a ratio above 1 -- a speed reduction. For output speed, invert: output = input speed times driver / driven. Example: a 20-tooth driver at 300 rev/min into a 60-tooth gear gives VR = 60 / 20 = 3, and output = 300 times 20 / 60 = 100 rev/min. Sprockets and chains count teeth the same way; pulleys use diameters.
Idlers, compound trains and belt choice
An idler gear reverses the output direction but does not change the ratio -- it depends only on driver and final driven teeth, so the idler cancels. In a compound gear train (two gears on one shaft) MULTIPLY the stage ratios: 2:1 then 2:1 gives 4:1. For belts: a flat belt slips; a vee belt grips a V-groove but cannot be crossed; a toothed belt or chain gives positive drive, tensioned by a jockey pulley on the slack side.
Drawn from real examiner reports.
Gear formula inverted or ratio reversed
The velocity ratio is driven / driver teeth; output speed is input times driver / driven. Candidates turn one upside down (VR as driver / driven), or state the ratio backwards, 1:5 for 5:1. Reason physically: a small gear driving a big one slows the output DOWN, so output must be smaller than input; if larger, you inverted the formula.
s22 Q11a(iii); w22 Q11c(iii)
Idler folded in; compound not multiplied
An idler changes rotation direction but leaves the ratio unchanged -- it depends only on driver and final driven gear. In a compound train (two gears on one shaft) MULTIPLY the stage ratios (2:1 times 2:1 = 4:1), then apply to the input speed. Candidates add the ratios, or use only the first stage, getting the wrong output speed.
s23 P43 Q11d
Belt tensioner on the tight or inner side
A drive-tension system uses a jockey (idler) pulley on a spring-loaded, adjustable arm against the belt. The mark is lost when it is drawn on the inner face or tight side. It must press on the outer face of the slack side, pushing the loose run inward to take up slack and increase the wrap; its position must be adjustable.
w23 P42/P43 Q10c
Vee belt treated as reversible
A vee belt wedges into the V-groove, gripping harder than a flat belt. Because it sits in the groove it cannot be crossed or twisted to reverse the pulley -- yet candidates suggest crossing it, or call it a positive, non-slip drive. It is not: a vee belt can still slip under heavy load. A toothed belt engages teeth for truly positive drive.
w23 P42/P43 Q10c
Flat belt where positive drive is needed
Asked why a camshaft or bicycle uses a toothed belt or chain not a flat belt, weaker answers just say it is stronger. The real reason: a flat belt can slip, so the driven shaft drifts out of step. A toothed belt engages pulley teeth and a chain the sprocket teeth, giving a positive drive that cannot slip, keeping input and output synchronised.
Teeth and diameters muddled
Gears and sprockets use tooth counts, but pulleys have no teeth so their ratio uses diameters. Candidates mix these up -- measuring a gear off the drawing, or counting teeth on a smooth pulley. The rule is otherwise identical: VR = driven / driver, output = input times driver / driven.
Worm and wheel can be back-driven
A testable wrong belief: that a worm-and-wormwheel drive works both ways, so the wheel could turn the worm. In fact it is non-reversible -- the worm turns the wheel, but the wheel cannot turn the worm. This self-locking behaviour holds a load when the drive stops (a tuning peg), and it gives a very large reduction in a single 90-degree step.
Lay the calculation out in stages
Transmission calculations are marked for METHOD. Write the formula, substitute the teeth or diameters, multiply the stage ratios of a compound train, then state the output speed with its unit (rev/min).
Sense-check the direction of the speed change
Predict which way the speed goes before calculating. A small driver into a large driven is a step-down, so output is SMALLER than input; the reverse is a step-up. If the arithmetic contradicts the gear sizes, you inverted the formula.
Teeth or diameters; ratio in asked order
Read whether the drive is geared or chained (use teeth) or a belt and pulley (use diameters), taking numbers from the question. Quote a ratio in the order asked, with a colon (3:1): stating 1:5 for a 5:1 reduction loses the mark.
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