(114.)
This contrivance, although in the main inferior to the more simple one of the crank, is not without some advantages; among others, it gives to the sun wheel double the velocity which would be communicated by the crank; for in the crank one revolution only on the axle is produced by one revolution of the crank, but in the sun-and-planet wheel, two revolutions of the sun wheel are produced by one of the planet wheel; thus a double velocity is obtained from the same motion of the beam. This will be evident from considering that when the planet wheel is in its highest position, its lowest tooth is engaged with the highest tooth of the sun wheel; as the planet wheel passes from the highest position, its teeth drive those of the sun wheel before them, and when it comes into the lowest position, the highest tooth of the planet wheel is engaged with the lowest of the sun wheel: but then half of the sun wheel has rolled off the planet wheel, and, therefore, the tooth which was engaged with it in its highest position, must now be distant from it by half the circumference of the wheel, and must, therefore, be again in the highest position; so that while the planet wheel has been carried from the top to the bottom, the sun wheel has made a complete revolution.
This advantage of giving an increased velocity may be obtained also by the crank, by placing toothed wheels on its axle. Independently of the greater expense attending the construction of the sun-and-planet wheel, its liability to go out of order, and the rapid wear of the teeth, and other objections, rendered it inferior to the crank, which has entirely superseded it.