Machine Kinematics
solved, then drawn
Concept

Ravigneaux — where it appears

A compound gearset with two suns of different sizes, two sets of orbiting gears meshing each other, and one ring. It is how a compact automatic gearbox gets four forward ratios from one gearset, and its ratios are the same plane-of-motions arithmetic with more members in it.

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

Also named here as simpson gearset — the same set of essays touches all of them, so they are one junction rather than several.

What a Ravigneaux gearset can be made to do. Every distinct ratio the gearset offers, as a reduction. Each one is the same mechanism with one more constraint imposed — a brake holding a member to the case or a clutch locking two members together — and the input is a choice as well, which is why a four-speed needs an input clutch rather than four brakes. The shaded rows are the 5 a real transmission on this gearset is sold with; the rest are ratios the mechanism has and the gearbox does not buy the elements to reach. Every value is exact: the reductions are ratios of integers and are printed as such.

Four speeds from two numbers

A Ravigneaux gearset has five tooth counts and gives seven exact ratios. Two of the counts do not appear in any of them — the short planet is an idler and its size is free — and the remaining three enter only through two dimensionless numbers, so the whole shift ladder of a four-speed automatic is a function of ring-over-sun and ring-over-the-other-sun. A Simpson three-speed is a function of one number.

transmission · Transmission The steps, against the ones the rule asks for. The design rule everybody quotes is that the steps between gears should be equal in ratio, so that the engine returns to the same speed after every shift. That makes the sequence geometric, and the ideal step for this spread over this many gears is 1.5324, marked. The steps a gearset actually gives are not free: the whole sequence is a function of the tooth counts, so once the top and bottom are chosen there is nothing left to spend on the middle. The worst step here is off the ideal by 10.8%.

The steps are not free

A gearbox is supposed to have equal steps between its gears, so that the engine returns to the same speed after every shift. A gearset has one or two numbers to spend on three or four gears, so from the third one the steps are a consequence rather than a choice — and asking for them to be equal turns out to be a quadratic whose root is the golden ratio, realised in tooth counts by consecutive Fibonacci numbers.

transmission · Transmission

Named alongside it

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

Catalogue numberDimensionless ratioEpicyclicSimpson gearsetTransmission relationVelocity ratioDesign ruleExact arithmeticGeometric progressionIdlerRatio stepsShift element

All concepts