mech quest?

Question

in ferguson paradox how it is that the two gears in mesh with planetary gear rotate in opposite direction?

Answer 1

In referring to it as a paradox, Ferguson was indulging in puffery. See the ref. The gear train on which it is based was part of an orrery, an 18th century mechanical representation of the earth orbiting the sun. As the arm carrying the earth revolved, a train of gears conveyed a relative rotation to the platforms carrying earth and its two reference circles. The first gear of the train was stationary, attached to the orbital center. The second or intermediate gear "walked" around the first gear and was connected to the third gear which was actually a set of three coaxial gears on coaxial shafts.
This last set produced three different effects. One gear had the same number of teeth as the central stationary gear; thus as the arm rotated, it maintained the same attitude with respect to the orrery dial. Another gear had a slightly greater number of teeth (probably 1 more) and rotated a part of a revolution less relative to each rotation of the arm. The third gear with fewer teeth rotated slightly more. These produced differential rotation of the earth and its two reference circles. One of the three was rotationally stationary while the other two moved slightly ahead of and behind it.
The ref. explains how Ferguson's ingenious mechanism became worked up into a paradox and a repudiation of religious nonbelievers.