Gears: separate speed, torque and direction
Work through tooth ratios, external-mesh reversals, idlers and ideal torque. Clear assumptions and complete examples; no hiring band.
This public guide explains one ideal-mechanics topic. Every completed attempt includes all five guides, alongside its correct count and five topic counts. It is not a personal attempt, performance band, percentile or occupational qualification.
The engagement assumptions come first
The gear tasks use ideal external gears on the explicitly described shafts, with no slip. Meshing gears pass the same number of teeth through their contact in the same time. That makes rotational speed inversely proportional to tooth count for the pair. The tasks do not silently introduce a belt drive, internal ring gear, compound shaft or slipping clutch. Those mechanisms can change the rule, so use the arrangement actually stated rather than a general impression that larger gears are always faster or stronger.
A fresh speed and torque calculation
Consider an ideal 20-tooth driver turning at 180 rpm and a 50-tooth driven gear. The driven speed is 180 × 20/50 = 72 rpm. If driver torque is 3 N m and tangential tooth force is conserved, driven torque is 3 × 50/20 = 7.5 N m. Speed and torque therefore use opposite tooth ratios. Their ideal power products match: 180 × 3 and 72 × 7.5 both equal 540 before the common rpm-to-angular-speed conversion.
Count external meshes for direction
Each external mesh reverses turning direction when all shafts are viewed from the same side. Two meshes reverse twice, returning to the initial turning sense; three reverse it. Count the contacts between gears, not just the number of gear bodies. A three-gear chain has two contacts. Stating the viewing side matters because looking from the opposite end reverses what clockwise looks like. The speed magnitude alone cannot tell you whether an answer’s direction has been tracked correctly.
An idler cancels only in the stated chain
Insert a separate 35-tooth idler between that 20-tooth driver and 50-tooth output. The ideal output magnitude remains 180 × 20/35 × 35/50 = 72 rpm. The idler’s tooth count cancels between the two speed ratios, but its own speed and the number of direction reversals still matter. This cancellation applies to a simple sequential chain on separate shafts. Do not extend it to compound gears sharing a shaft without drawing and calculating the new arrangement.
A topic count does not measure design skill
The six gear answers contribute six possible correct marks, and the report shows which original statements were answered correctly. A total alone cannot identify whether a miss involved an inverted ratio, a unit or a direction reversal. Read that item’s working before choosing a new example. All five complete topic guides remain available at every count. The result is not a calibrated test of CAD work, maintenance competence, mechanical aptitude relative to other people or suitability for an engineering occupation.
Check an answer through invariants
For speed, multiply each speed by its gear’s tooth count and compare the products within a meshing pair. For ideal torque, compare torque divided by tooth count when the same tangential force is assumed. For direction, write a small clockwise/counterclockwise list at each successive contact. Keeping those three checks separate is more reliable than combining a remembered “gear ratio” phrase with an uncertain numerator. Practise with fresh tooth counts so a correct answer does not depend on recognising this bank’s numbers.
Ideal transmission is not measured machinery
Lossless torque ratios explain an ideal exchange of speed for torque, not free energy. Actual systems involve friction, tooth contact, bearing losses, backlash, loading and structural constraints that are absent from these questions. The bank does not measure those quantities or establish safe machine settings. Its untimed format also provides no reaction-time or speed norm. Use the calculation and its explicit assumptions as the learning object; neither a perfect score nor a changed repeat score certifies practical machine performance.