Mechanical Power Transmission Systems
Ratio rules everything
For belts, chains and gears the speed ratio is the ratio of driven size to driver size: rpm_out = rpm_in × (driver / driven). For gears use tooth counts or pitch diameters; for V-belts and chain use pitch diameter, not outside diameter. Torque moves the opposite way: a reduction in speed multiplies torque by the same ratio, less losses.
Drives in detail
V-belts need correct tension and matched sheave grooves; a glazed or worn sheave destroys belts. Chain sag is typically about two to three percent of span, with lubrication reaching the inside of the links. Gear trains are judged by backlash and contact pattern rather than by sound alone; helical gears run smoother than spur, bevel gears change shaft direction, and worm drives give high reduction with low efficiency and possible self-locking. Couplings are rigid or flexible; flexible types absorb misalignment but still require alignment. Clutches and brakes need clearance and friction-surface condition checked together.
Worked example
A 1750 rpm motor drives a 5 in. sheave connected to a 12 in. sheave. Output speed = 1750 × 5/12 = 729 rpm, and available torque rises by 12/5 = 2.4 times, minus drive losses. Reversing the fraction is the classic wrong answer.
Traps
Inverting the ratio; using outside diameter instead of pitch diameter; over-tensioning a belt until bearing life collapses; reading a gear contact pattern that shows edge loading as normal; assuming a worm drive can be back-driven.