Planetary Gear Sets — How Sun, Planet, and Ring Gears Create Transmission Ratios

The Basic Planetary Design

A simple planetary gear set has three members: the sun gear, the planet carrier, and the ring gear. The sun gear is a small external-tooth gear at the center. The planet gears (typically three or four of them) surround the sun gear and mesh with it on their inner circumference. The planet gears are mounted on pins in the planet carrier, which can rotate around the sun gear centerline. The ring gear is a large internal-tooth gear that surrounds everything — the planet gears mesh with its inner circumference.

The key feature is that all three members are always in mesh — the planet gears are always in contact with both the sun gear and the ring gear simultaneously. This means that if any two members are defined (driven or held), the third is completely determined by the gear geometry. There is no selecting gears by sliding collars — the gears are always meshed. What changes is which member receives input power, which is held stationary (by a clutch pack or band), and which delivers output.

How Different Ratios Are Produced

The gear ratio produced by a planetary set depends on the tooth counts of the ring gear and sun gear. The planet gear tooth count affects their physical size but not the fundamental ratio between input and output. The ratio formula for a simple planetary with ring gear held:

If the sun gear is the input and the planet carrier is the output (ring gear held): Ratio = 1 + (Ring Teeth / Sun Teeth). So a ring gear with 72 teeth and a sun gear with 36 teeth produces 1 + (72/36) = 1 + 2 = 3.0:1 reduction. The planet carrier (output) turns once for every three sun gear (input) turns.

If the ring gear is the input and the planet carrier is the output (sun gear held): Ratio = 1 + (Sun Teeth / Ring Teeth). Same 72/36 example: 1 + (36/72) = 1 + 0.5 = 1.5:1 reduction. A smaller reduction — the ring gear is a slower input to begin with.

If the planet carrier is the input and the ring gear is the output (sun gear held): Ratio = Ring Teeth / (Ring Teeth + Sun Teeth) — this produces an overdrive ratio less than 1:1. Same example: 72 / (72 + 36) = 72/108 = 0.67:1 overdrive. The output ring gear spins faster than the input planet carrier.

Direct Drive and Reverse

Direct drive (1:1 ratio) is achieved when any two elements of the planetary set are connected together. If the sun gear and the ring gear both receive input power (rotating at the same speed), the planet gears have no relative motion to either — they are locked between them — and the planet carrier must also rotate at that same speed. No ratio multiplication, no reduction — the input equals the output. This is why direct drive in a traditional 3-speed automatic (3rd gear) was called "direct" — there was no gear reduction at all, just a direct mechanical connection.

Reverse is produced by holding the planet carrier stationary while driving the sun gear — the planet gears orbit against the stationary carrier and drive the ring gear backward (opposite to the sun gear input direction). The ratio is negative — the ring gear output rotates in the opposite direction from the sun gear input. The magnitude of the reverse ratio is Ring Teeth / Sun Teeth — typically between 2.0:1 and 3.0:1 in most transmissions.

Compound Gear Sets — More Ratios, Same Space

A single simple planetary set can produce a maximum of one forward reduction, one overdrive, one direct drive, and one reverse — not enough for a modern 6, 8, or 10-speed automatic. Compound gear sets combine two or more simple planetary sets, often sharing members between them, to produce many more ratios from a compact package.

The three most important compound planetary designs in automotive history are the Simpson, the Ravigneaux, and the Lepelletier. Understanding these designs explains why certain transmissions behave as they do and why certain failure modes appear in specific gear positions.

The Simpson Gear Set

Howard Simpson patented the Simpson gear set in 1955 and it became the basis for most American 3-speed automatic transmissions — the GM Turbo-Hydramatic 350, 400, and 700R4 (4-speed variant), the Ford C4, C6, and many Chrysler A-904 and A-727 units. The Simpson design uses two simple planetary gear sets that share a common sun gear shaft. The front planetary's ring gear is the input; the rear planetary's ring gear is the output (to the output shaft); and the shared sun gear connects them.

By applying different combinations of bands and clutches to hold or connect the front ring gear, the rear ring gear, the sun gear, and the planet carriers, multiple forward ratios and reverse are produced from this simple, compact arrangement. The shared sun gear is a key structural element — sun gear shaft failures are a known failure pattern in worn Simpson-based transmissions, as the sun gear carries significant load in multiple gear positions.

The Ravigneaux Gear Set

The Ravigneaux gear set combines two planetary sets that share a common ring gear and a common planet carrier, with two sun gears (a small front sun and a large rear sun) and two sets of planet gears (short planets that mesh with the front sun, and long planets that mesh with both the rear sun and the ring gear). This arrangement produces more ratios than a Simpson set from a similar package size.

Ravigneaux-based transmissions include the Ford FMX and some Honda units. The Ravigneaux set is also used as one half of the Lepelletier design. The two-sun-gear arrangement means that failures of either sun gear or their supporting components affect specific subsets of gear positions — useful diagnostic information when a transmission drops out of specific gears but works in others.

The Lepelletier Gear Set

The Lepelletier arrangement — patented by Frenchman Germain Lepelletier in 1992 and widely adopted in the 2000s — combines a simple planetary front set with a Ravigneaux compound rear set, with the front planetary's planet carrier driving the Ravigneaux sun gear. By using six friction elements (clutch packs and brakes), this design produces six forward gear ratios and one reverse from a package that is smaller and lighter than stacking three or four simple planetary sets.

ZF adopted the Lepelletier design for their 6HP series (6-speed rear-wheel-drive automatic used in BMW, Audi, Jaguar, Land Rover, and many others). Aisin used similar principles in their 6-speed units. The Lepelletier was the key technical enabler of the industry-wide shift from 4-speed to 6-speed automatics in the mid-2000s — it provided two additional ratios without requiring a significantly larger or heavier transmission. The 8-speed and 10-speed successors use more complex compound arrangements based on similar principles, with additional planetary sets and friction elements.

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