In message #1577 posted to the Yahoo! Prius_Technical_Stuff discussion group, Al, the Harley-Prius guy, says that he "never had a problem understanding that power-split unit, once [he] realized that it was a variation of something that [he] had come to understand many years ago" - an automobile's differential. He goes on to explain the Toyota Prius planetary gear arrangement in the PSD in terms of the differential, which is also a three-shaft gear device. Al has very kindly allowed me to extract and rephrase his message to help anyone who is still puzzled after reading my explanation or who just wants to look at it in a different way. Although we'll start with a review of the differential, this approach to the PSD will be most useful if you already understand what an automobile's differential does and how it works.
First, a quick (or wordy, you tell me) refresher on the differential gear-set (that's right, the mechanism that allows wheels to turn at different speeds when we go round a corner): a differential gear-set is a "box" with three rotating shafts; the vectored action of one shaft directly relates to the SUM of the vectored actions of the remaining shafts. (By vectored, I mean that the direction of rotation is important.) This gear-set offers an infinite number of wheel speed differences by placing a differentiating unit (pinion gears and their carrier) between the two wheel shafts. The remaining interface shaft is connected directly to the differentiating unit. Bevel gears let us orient the shafts as needed.
During normal straight-line driving, both wheel shafts rotate equally in a given direction. To do this, the entire differentiating unit rotates, yet the little pinion gears within it are not rotating on their little shafts. When the automobile is rounding a bend, one wheel shaft must rotate slightly faster than the other. To do this, the little pinion gears must rotate slowly on their little shafts within the differentiating unit, which itself is rotating. Finally, if you were to jack both driven wheels off of the ground, and prevent the transmission shaft from turning (motor off with automatic transmission in park or manual transmission in gear), you would find that if you rotate one wheel in one direction, then the other wheel rotates in the opposite direction. To accomplish this, the little pinion gears are spinning within the stationary differentiating unit.
So, imagine that a differential gear-set is cut open and made of clay, in order that you can stretch, twist, and reconfigure components somehow, but without affecting the relationship they have among themselves. Conceptually, create a Prius power-split device by:
Since there's room, add two more planet gears, and voila!
In short, a planetary gear-set IS one kind of differential gear-set, a kind devoid of bevel gears. Moreover, a planetary gear-set presents more useful proportional relationships among elements through careful selection of ring-to-pinion gear ratio and pinion-to-sun gear ratio.
It works the other way, too. Some readers may find that if they imagine a Prius with a differential for its transmission, the workings are a snap: put MG2 (drive motor) on one axle, put MG1 (ICE generator) on the other axle, and attach the ICE to the propeller-shaft yoke. Despite what MG2 might be doing with the tires, even if you are going backward in reverse, the ICE and MG1 together will take care of other business at hand (charge a battery, run a compressor, stay warm, whatever).