Machine Kinematics
solved, then drawn
Concept

Planetary — where it appears

A gear train whose orbiting members are carried round a central gear on an arm, so that three shafts share one equation. The one equation in three rates is what makes it a two-freedom mechanism, and every quoted ratio for one is that equation with a second condition supplied.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Sun 24, ring 72, planet 24. An epicyclic train has three shafts and one equation relating them, so fixing any one gives a different ratio from the same gears. With the ring held, a sun input turns the carrier at 1 + 72/24 = 4.000 to one. Willis's equation and the tabular superposition method are independent derivations and both are computed here; the site requires them to agree, because planetary ratios are the most commonly mis-stated numbers in mechanism work and the sign errors are notorious.

Epicyclic ratios, two ways

An epicyclic train has three shafts and one equation relating them, so fixing any one gives a different ratio from the same gears. The sign errors are notorious, so every ratio here is computed by Willis's equation and by the tabular method, and the two are required to agree.

gears · Tooth A reduction made out of a difference. A compound epicyclic's reduction is 1/(1 − z₁z₄/z₂z₃) — a ratio of two integers, so it is exactly what a catalogue says, at every position, forever. It is the only number in this field that survives being measured, and the reason is that it is a count. What it is not is insensitive: each row's denominator is a difference of two nearly equal products, and the last two rows differ by one tooth on one ring.

A ratio that is a count

A compound epicyclic's reduction is a ratio of two integers, because it is a ratio of tooth counts — 2176/106 for the drive here, exact at every position and on every unit ever made. It is the only quoted number in this field that survives being measured, and it is fragile in a way exactness does not protect against: one tooth on one ring moves it by forty per cent.

applied · Tooth

Named alongside it

The objects these essays reach for when they reach for this one.

EpicyclicMeshRatioConditioningConstraintInvoluteMobilityReductionSensitivitySuperpositionToothVelocity ratio

All concepts