This article aims to show how a 'canonical' (3-speed) automatic transmission gearbox works, using interactive animations.
The "heart" of an automatic transmission is the epicycloidal or planetary gearset. This kind of gearset has the interesting feature of changing gear ratios without having to engage or disengage individual gears. This allows for smooth gear changing even under load and without clutch.
The following video shows a planetary gear, and how locking one part makes the others turn in a different pace:
A planetary has three main parts: sun (center gear), planets (small gears turning around the sun), and ring or annulus, that is also engaged with planets by the outer side.
The video does not show it, but planets are supported and tied together by carrier. The rotation of planets themselves are not important; the rotation of the planet carrier itself is useful for reduction.
A 'canonical' Simpson automatic gearbox has two interconnected planetaries. The next video shows it configured to first gear:
In this gearbox, the planet carrier of first gearset is connected to second gearset's ring (in video, both are green because of this). They are connected by an axle, which is also the output axle of the gearbox to the wheels.
A planetary gear keeps rotating if one part is blocked. Locking different parts makes the gear deliver different gear ratios.
It is easier to look the planetary as a "black box", and play with it. The animation below is exactly for that.
You should press "Lock" or "Engine" buttons for at least two axles. The third one becomes the output and turns blue. Relative speeds show the obtained the gear ratio.
You may connect two axles to engine, and both turn red. In this case, there is no reduction; output turns exactly at the same speed as the inputs.
There are many possibilities: you can get outputs that are slower, faster and/or reversed in relation to engine RPM.
A planetary gearset is comparable with a differential, which is also a three-axle box, and output of one axle depends on other two.
Another nice feature of planetaries is that transitions are smooth. When an axle is locked, it does not happen instantaneously, but it's not a problem; gear ratio changes smoothly.
Actually, this feature can be leveraged to implement a CVT (continously variable transmission), using a single planetary and an eletric motor. The Toyota Prius hybrid car employs this approach.
So, instead of just locking an axle or connecting it to the engine, the eletric motor is used to turn it over a wide range of RPMs, including reverse, to obtain any gear ratio in output.
The animation below simulates such a CVT. You can control motor RPM in order to obtain any output RPM, including zero.
Sun: electric motor
RPM: 0% of engine RPM
Well, let's crawl back to our world of conventional gearboxes, where planetary elements can only be engaged to engine or locked.
Given these two options, a single planetary yields three gears: two forward (with and without reduction), and reverse. The "canonical" automatic gearbox has two planetaries, three gears forward and one reverse.
The following animation "implements" a Simpson gearbox, one button for each gear. See how components are locked or engaged to obtain the desired output:
In this animation, axle(s) engaged to engine is/are colored red, to make it clear where the mechanical power comes from.
You will notice that engine may be engaged to a) first set's ring; b) sets' suns (both suns share the same axle); c) to ring and suns (third gear); d) to none of them (neutral).
Once upon a time, cars had an additional overdrive gearbox after the main gearbox, to "stretch" the highest gear, reducing engine RPM and saving some fuel in the highway.
The overdrive was commonly implemented with a single planetary, but using it to increase output RPM instead of reducing it. The animation below "implements" an overdrive:
It's been 30 years since automatic transmissions absorbed the overdrive. The most common configuration since then has been three planetaries (two acting 'canonically' and one as overdrive) yielding four forward gears.
A more complex project can squeeze five gears from three planetaries. In fact 5-speed and 6-speed boxes are getting common.