Who invented the "planetary gearset" and when?  A simple version of
this gear set, which allows gear reduction and gear reversal, was used
in the Ford Model "T" and a compound version is now used in virtually
all modern automatic transmissions.

Hello mahvin-ga,

I don?t know if the planetary gearset is the same is the planetary
transmission, but the website below claims that Alanson P. Brush has
the patent on the planetary transmission.

Cadillac History
1902-03 CADILLAC
 http://100megsfree4.com/cadillac/cad1900/cad03s.htm
?Alanson P. Brush held the patents on the copper water jacket,
variable lift intake valve, mixer, planetary transmission, and
adjustable rack and pinion steering. By 1906, the impact of the Brush
patents would start a drastic change in Cadillac design.?



There?s another reference to Alanson Brush and the planetary
transmission at the following link:


Car-nection.com
The (new) Cadillac Database
http://www.car-nection.com/yann/Dbas_txt/Cad05-12.htm
Henry Leland directed the assembling of the cars with Alanson P.
Brush, the designer. The planetary transmission, controlled by a
single lever, enabled the Model D to be propelled quickly to speeds of
45 or 50 mph without any gear changing.



Googlenut

It may have been much earlier than we think:

http://www.ancientx.com/nm/anmviewer.asp?a=28&z=1

At least 20 gear wheels of the mechanism have been preserved,
including a very sophisticated assembly of gears that were mounted
eccentrically on a turntable and probably functioned as a sort of
epicyclic or differential, gear-system.

NOTE: epicyclic is another name for planetary gearing.