Simpson planetary gearset
The Simpson planetary gearset consists of two planetary gearsets, both having the same gears and gear ratios. It was employed in automatic transmissions. It was one of the several designs invented by American engineer Howard Simpson. A Simpson gearset delivers three forward gears and one reverse, plus neutral. Actually there are four forward gears, but two of them have exactly the same ratio, so there are three distinct gears. Third gear is always direct drive (1:1).
Overview
The two identical planetaries are interdependent. Their suns are bonded - in practice, both gearsets share a longer sun gear. The planet support of the first gearset ("first" meaning closer to engine input shaft) is in synchronism with the second gearset's ring, and both are in synchronism with the output shaft.
Due to these links, two bands and two clutches are all that is needed to command the gearsets and extract the different gears. As many as six forward gears can easily be developed from a Simpson box, just by adding a third gearset (underdrive or overdrive) which is operated independently, to create two ranges for each gear.
First gear
In Simpson's gearbox, the first gear is the most difficult to understand, and probably the one that causes most stress in the components. It happens because there is a feedback: the first gearset actuates on the second gearset and output shaft; the second gearset reacts and makes the sun turn in reverse, causing the first gearset to increase the reduction ratio. The mechanical energy has actually to "loop" in the gearset system until settling the ratio.
Gear changing
Another problem of changing from first to second gear is that two bands must actuate in synchronism: the planet support of the second gearset must release at the same time as the sun band is actuated. As a result, this is a gear change that tends to be rougher than the others, where just one band is released or actuated. This also means more wear in auto box parts. This is solved by the use of one-way overrun clutches which allow one or more components to "free wheel" when the transmission shifts into a higher gear. GM's Turbo Hydra-Matic 350 and 400 transmissions utilized overrun clutches in both the low and intermediate gears, allowing for fully progressive shifting with no "overlap".
Due to both factors abovementioned, gear changing patterns in some Simpson gearboxes, including modern 4-speed units, avoid first gear as much as they can, going up to 2nd as soon as possible, and especially avoiding reducing to 1st unless absolutely necessary (very slow speed plus floored throttle).
Modern gearsets
The Simpson gearset is now more or less obsolete. Other gearsets can make 4 forward gears with just two planetaries. Most modern gearboxes employ the Ravigneaux planetary gearset design, which produces 4 forward gears from a single set, or a Lepelletier gearset which provides 6 or more forward gears by adding another standard planetary to the Ravigneaux gearset.
Nevertheless, some new cars are still sold with automatic transmissions based on the Simpson gearset. Such transmissions are typically four-speed, designed in the late 1990s, they are electronically controlled versions of older projects, and are kept in production because they are cheap, reliable, well-known and good enough for the target application.