Secrets of the Simpson Gearset


Presenting a detailed history and description of each production transmission to use a Simpson gearset is well beyond the scope of this article. However, we will explain the basic principles of its operation, which will help you understand the production applications and their relatively minor variations on the theme.

A simple planetary gearset has three elements: a sun gear, a set of planet pinions journaled on a planet carrier, and an annulus (ring gear). All the gears are in constant mesh: The planet gears mesh with the sun gear and the annulus meshes with the planets. Obviously, the planet carrier is not a gear; rather, it’s the armature holding the pins on which the planet gears rotate, which may itself rotate at a different speed than the planets, the sun gear, or the annulus.

Color diagram of a simple planetary gearset © 2017 Aaron Severson

A very basic schematic of a simple planetary gearset: The annulus, also known as a ring gear or internal gear (green), meshes with planet pinions (gray) on a planet carrier (purple). Those planets mesh with the central sun gear (orange). (author diagram)

A Simpson gearset is a compound planetary gear train with five elements: the annulus of gearset A (which we’ll abbreviate AA); a set of planet pinions on the planet carrier of gearset A (which we’ll abbreviate CA); the sun gear (S); the annulus of gearset B (AB); and another set of planet pinions on the planet carrier of gearset B (CB). Annulus B is permanently affixed to the output shaft.

Color diagram of a Simpson gearset in neutral © 2017 Aaron Severson

This diagram shows one version of the Simpson gearset, with two multi-disc clutches and two brake bands. All are shown here in a neutral condition. Note that both gearsets share the same sun gear (orange). In Simpson’s earliest independent transmission designs, there were two separate sun gears that turned together only in the forward gears; reverse locked the rear sun gear to the input shaft while allowing the front sun to turn backward. By 1951, Simpson had decided this was undesirable because it caused too much friction, a problem resolved by using a single common sun gear. (author diagram)

(To be clear, what we’re describing as “gearset B” is the gearset whose annulus is connected to the output shaft, regardless of actual physical position. Depending on the specific layout, gearset A may be located behind gearset B or vice versa; this description and all the calculations below are based on each gearset’s function, not its position.)

Color diagram of Simpson gearset with intermediate shaft © 2017 Aaron Severson

This diagram illustrates another variation of the Simpson gearset, this one with gearset A at the back of the transmission, driven by the intermediate shaft, and interconnected carrier A and annulus B (both purple). (author diagram)

Any Simpson gear train requires at least two brakes and two clutches:

  • A forward clutch that connects the input shaft to annulus A in the forward gears. (In some variants, annulus A is permanently connected to the input shaft and the forward clutch instead connects planet carrier A to the output shaft.)
  • A direct/reverse clutch that connects the input shaft to the sun gear in third and reverse. (Simpson also designed some split torque variants where this clutch instead connects the sun gear directly to the engine, usually through the torus cover of the fluid clutch.)
  • A low/reverse brake that can hold planet carrier B stationary in certain gears.
  • An intermediate brake that can hold the sun gear stationary in certain gears.

We say “at least” because some transmissions use multiple brakes of different types, a point we’ll discuss in more detail below.

Color diagram of Simpson gearset with permanently connected first annulus © 2017 Aaron Severson

This diagram shows a third version of the Simpson gearset in which annulus A is permanently connected to the input shaft (medium blue). The forward clutch connects carrier A (light green) to annulus B and the output shaft (purple). (author diagram)


Simpson gearsets obtain three forward and one reverse speed by combining the above elements in the following combinations:

  • First (low): The forward clutch engages, allowing the transmission input shaft to drive annulus A (or connecting planet carrier A to the output shaft). A low/reverse brake is applied to planet carrier B. As annulus A rotates, reaction torque created by the inertia of carrier A causes the sun gear to turn backward. The sun gear’s reverse rotation attempts to turn planet carrier B backward as well, but the low/reverse brake holds the second carrier stationary instead. This causes annulus B to rotate around the stationary carrier in the opposite direction — which in this case is forward — at reduced speed. Since carrier A is also affixed to the output shaft, it must also rotate forward at the same speed.
  • Second (intermediate): The forward clutch remains engaged, so the input shaft continues to drive annulus A forward. The low/reverse brake disengages, allowing planet carrier B to rotate freely. An intermediate brake is applied to hold the sun gear. As annulus A rotates, reaction torque attempts to turn the sun gear backward, but the brake holds the sun gear stationary instead. This forces planet carrier A — and the output shaft — to rotate forward around the now-fixed sun gear at reduced speed. The rotation of the output shaft drives annulus B forward at the same speed, causing planet carrier B to rotate idly forward around the stationary sun gear.
  • Third (high): The forward clutch is still engaged, allowing the input shaft to drive annulus A. Both the low/reverse and intermediate brakes are released, allowing planet carrier B and the sun gear to rotate freely. The direct/reverse clutch engages, locking the sun gear to either (depending on the version) planet carrier A or annulus A. This forces all elements of both gearsets to turn at the same speed, putting the transmission in direct drive. (In split torque variants, the sun gear turns at engine speed, annulus A turns at input shaft speed, and carrier A resolves the difference.)
  • Reverse: The direct/reverse clutch engages, allowing the input shaft (or, in split torque versions, the torus cover) to drive the sun gear forward. A low/reverse brake is applied to hold planet carrier B. The sun gear’s rotation attempts to turn carrier B forward, but the brake prevents the carrier from moving, forcing annulus B to rotate backward at reduced speed. The forward clutch is released, disconnecting annulus A from the input shaft (or, if annulus A is permanently connected to the input shaft, disconnecting carrier A from the output shaft) so that gearset A can’t transmit any torque. (If annulus A is released, it spins idly backward; if the planet carrier A is disconnected, it turns idly forward at engine speed or close to engine speed.)
  • Neutral: All clutches and brakes are released. No element is connected to the input shaft (or the torus cover) and no element is held.


In principle, a Simpson gearset can use any type of brake or clutch; Simpson’s earliest versions of this layout used cone and dog clutches along with band brakes. Most production applications use a mix of multi-disc clutches, band brakes, and one-way clutches.

Unlike other types of brake, which keep the elements to which they’re attached from turning in either direction, a one-way clutch (or overrunning clutch) allows a gear element to rotate in one direction, but not the other. Many Simpson gear trains (and other automatic transmission layouts) use sprag-type or cam-and-roller one-way clutches to simplify the mechanics of shifting.

For example, you’ll notice in the above summary that in first gear, the sun gear of a Simpson gearset rotates backward (i.e., opposite the direction of engine rotation and attempts to rotate planet carrier B backward as well. In second gear, carrier B rotates idly forward. If carrier B is connected to a one-way clutch that allows it to turn forward but not backward, that clutch will hold carrier B stationary in first and automatically releases upon the shift to second, or vice versa. The one-way clutch requires no external mechanism or synchronization.

Color diagram of a Simpson gearset with a one-way low clutch © 2017 Aaron Severson

Many Simpson gearsets use a one-way clutch to hold carrier B (dark red in this diagram) stationary in first gear with allowing carrier B to rotate forward in second and third. In this diagram, the one-way clutch is indicated in fuchsia with a black arrow signifying that the clutch allows the carrier to rotate forward, but not back. (author diagram)

There are two drawbacks to using a one-way clutch in this way. First, the one-way clutch isn’t effective in reverse, when the forward rotation of the sun gear attempts to rotate carrier B forward. Second, if the output shaft overruns the engine (for example, when descending a steep hill in first gear), the rotation of annulus B will also rotate carrier B forward, causing the one-way clutch to immediately unlock and leaving the transmission effectively in neutral. Consequently, the one-way brake must be supplemented by a band or clutch-type brake, which is used in reverse or when the driver manually selects “Low.”

Some transmissions with Simpson gearsets, such as the Chrysler TorqueFlite, use both a one-way clutch and a separate brake for first gear, but only a single band- or clutch-type intermediate band for second. To use a one-way clutch to hold the sun gear in second, there must be some means of neutralizing that clutch in first gear, when the sun gear has to turn backward. Simpson proposed doing that by attaching the outer race of the one-way clutch to a brake drum and band brake. Reverse rotation of the sun gear would always lock the inner race against the outer race, but with the brake released, the whole drum would simply rotate backward. Some production transmissions, including the GM Turbo Hydra-Matic, accomplished the same effect by using a multi-disc clutch to lock the one-way clutch’s outer race to the transmission case.

Color diagram of the sprag clutches in a GM Turbo Hydra-Matic 400 transmission © 2017 Aaron Severson

As shown in this diagram, GM’s Turbo Hydra-Matic uses one-way sprag clutches (fuchsia with black arrow) for both first and second gears. The rear sprag allows carrier B (dark red) to turn forward, but locks if carrier B attempts to turn backward. The intermediate sprag allows the sun gear (orange) to rotate forward, but locks if the sun gear turns backward. If the intermediate clutch is released, the sprag will turn backward along with the sun gear, but if the intermediate clutch is engaged, the sprag’s outer race is locked to the case. (author diagram)

As with a one-way clutch on carrier B, a separate overrun or coast brake is still needed to keep the sun gear locked when coasting. Turbo Hydra-Matic included an overrun band for this purpose, functional only when manually selecting a lower speed range and disengaged in Drive. This gave the driver greater ability to keep the transmission in second gear for engine braking in hilly terrain.

While this arrangement is obviously more complex than a simple two-brake/two-clutch Simpson gearset, it allows each shift in Drive to be accomplished by engaging or disengaging one element. In a Turbo Hydra-Matic, for example, engaging the forward clutch from a neutral condition would give first gear; also engaging the intermediate clutch would give second; and engaging the forward, intermediate and direct/reverse clutch gave third. Downshifts were just as straightforward; from third, releasing the direct/reverse clutch would produce an immediate downshift to second and then releasing the intermediate clutch put the transmission back in first. The additional mechanical complexity was repaid with simpler (and usually smoother) shift action between all forward speeds.

On the following page, we’ll explain how a Simpson gearset’s ratios are calculated.


Add a Comment
  1. Thank you for continuing this fascinating exploration of the technical details and history of automatic and semi-automatic transmissions. I’ve been interested in cars since 1985 when I was finally within reach of driver’s license age and I have read quite a bit of the engineering history of the automobile but I still had no idea of the variety of designs that the American manufacturers put on the road before getting to what I always thought of as the norm – three speed plus reverse, torque converter coupled automatic with the PRND21 shift pattern. I had read references to “slip and slide with Powerglide” but the only car I ever drove with an automatic that was different from the C4/C6/Turbo-Hydramatic/Torquflite experience was a VW Beetle with the semi-automatic transmission. I hope you do an article on pre-selectors someday too.

    1. In fact, I was just looking at some stuff about the Wilson preselector, which is an ingenious device.

      Part of the reason I’ve written so much about Hydra-Matic is that I was amazed at how the earlier versions have fallen into obscurity — which is amazing when you consider their production volume. Most mechanically inclined automotive people are probably still reasonably familiar with Turbo Hydra-Matic, TorqueFlite, and the C4/C6, but the older ones are now poorly understood (and some, notably the dual- and triple turbine torque converter transmissions, weren’t that well understood when new!).

  2. My daily driver (by choice) is an ’89 Wrangler. Probably one of the last applications of the classic Torqueflite. Three speeds, no lock up, no overdrive, no electronics. Not all that efficient, but over 300k with a single tear down for new seals.

  3. Another system that saw service with UK’s BMC and its later incarnations was the 4 speed AP (Automotive Products) automatic transmission.
    When it was working properly it was an excellent transmission, making automatic versions of the original Mini and Austin 1100 (sold as the Austin America in the USA), and the Austin Maxi. The Mini and 1100 models suffered very little performance penalty compared with stick cars, the Maxi had a 5 speed stick shift, so the automatic suffered in comparison.
    The designers managed to cram it underneath the engine as in the stick transmission. Even more remarkably, they persuaded it to work sharing the engine oil. However the latter may have proved not such a great idea, they had a very short lifespan, typically 30-40,000 miles. If it had its own separate lubrication I think that would have helped improve its durability.
    It has long been confined to history now, like so many British innovations lack of investment and development meant it fell by the wayside.

    1. I know of the AP automatic, and of the earlier AP Manumatic, but I confess I haven’t ever investigated its innards!

  4. Thank you for taking the time to explain all of this as well as you do. I’ve poked my head around inside a few automatic transmissions but never to this level of detail.

    Of note: You could still find this same layout in use in 2001. Chrysler was unable to prevent their Electronic Ultradrive 40TE from overheating in the Neon compact car. It was then fitted it with the 31TH(A413) TorqueFlite from 1995-2001. A version of the A904 TorqueFlite with a transfer gearset on the output shaft to connect the power back to a center mounted differential due to the cars transverse layout. The only electronics was a solenoid to engage the lockup clutch in the torque converter. Sadly even the high stall converter used couldn’t overcome the fact that you didn’t shift to 2nd gear until 55mph. Giving the car a reputation of being painfully slow.

    1. Yeah, the TorqueFlite survived a remarkably long time, although it really ended up dragging down the image of the Neon (especially in the U.K.).

  5. A small nitpick (hope you don’t mind): On page 3 you surmise that a transmission could have 88, 40 and 24 teeth on its gears. While this is mathematically feasible, engineering practice shows that such an arrangement would result in severe and uneven wear of the gears in question. The preferred arrangement is a hunting tooth arrangement – no common denominator for the gears in contact, ensuring even wear.

    (Imagine a gear whose last tooth was not given the final pass during machining, resulting in a slight profile shift of the tooth. If it were always in contact with 1 or 2 teeth on the opposite gear these would wear rapidly, resulting in an uneven transmission of force as they mesh and come out of contact, which in turn would increase the wear rate even more.)

    1. I hadn’t considered that point when I wrote that section, but you’re right. I should probably see again if I can find actual gear teeth counts, which would be the best solution.

    2. Okay, I was able to determine now that the transmission in question (early TorqueFlite) had actual gear teeth counts of 62, 21, and 28 teeth, giving ratios of 2.452/1.452/1.000 and -2.214, and I’ve amended the text accordingly.

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