In this example, the arm velocity was given. If it is to be found as the output, then it must
be entered in the table as an unknown, x, and the equations solved for that unknown.
FERGUSON’S PARADOX Epicyclic trains have several advantages over convention
al trains among which are higher train ratios in smaller packages. reversion by default. and
simultaneous, concentric, bidirectional outputs available from a single unidirectional in
put. These feawres make planetary trains popular as automatic transmissions in automo
biles and tmcks, etc.
The so-called Ferguson’s paradox of Figure 9-38 illustrates all these features of the
planetary train. It is a compound epicyclic train with one 20-tooth plane gear gear 5)
carried on the arm and meshing simultaneously with three sun gears. These sun gears
have 100 teeth (gear 2), 99 teeth (gear 3), and lOI teeth (gear 4), respectively. The center
distances between all sun gears and the planet are the same despite the slightly different
pitch diameters of each sun gear. This is possible because of the properties of the invo
lute tooth form as described in Section 9.2p. 434). Each sun gear will run smoothly with
the planet gear. Each gearset will merely have a slightly different pressure angle.