family of diagrams, meshing gears are represented by
tangent circles. In this case the upper and lower
gears and the pinion must be bevel gears, with
teeth at a 45-degree angle to the face. Notice that
since the three discs are stacked, the blue axle
must be threaded through one of the outer ones.
Such a device, usually incorporating several pinions,
is called a Simple bevel-gear differential;
the blue axle is the "spider shaft take-off."
This mechanism is a rotary form of the straight-line
differential: imagine folding the purple and green racks
back and bending them into equal circular gears. The slider
folds over to a disc of the same radius; now the pinion
is attached to its circumference.|
Let us count counter-clockwise
rotation as positive, since it correponds, in this interpretation,
to the racks moving to the right. Since the three wheels
have the same radius, their rotational speeds a (top),
b (bottom) and c (central blue disc) must
still satisfy c=(a+b)/2.