Page:The Kinematics of Machinery.djvu/451

 EPICYCLIC TRAINS. 429

wheel a to be movable about 1, move it by the crank c, carrying with it &, through any angle o>, and then leaving c in its new position turn a back into its old one. Then any diameter of the wheel I will have first turned through an angle o> from its original

position, and will then (considering the diametral ratio =- of the

wheels) have been further turned through an angle of = x a), both

rotations taking place in the same direction as that of the arm, so that the whole angular motion of I has been :

a\

If for any given time, as a minute, w n.^ir and G>' n'.27r, we have for the relative number of revolutions of the wheel and the

arm:

n

If either of the wheels were annular, then the turning back of a into its original position would diminish instead of increasing the angular motion o>' of b, so that we should have

1 _ - n I

Such a mechanism as that before us is known generally as an epicyclic train. It is frequently applied in practice in the form shown, but more often still in a different shape, that namely of a reverted epicyclic train.

If we place the reverted train (G zZ C^'), already considered in the last section, upon a, as is shown in Fig. 282, we can find the velocity of the turning link I c by the foregoing method. It is now necessary however to find the motion of the wheel d (conaxial with a) relatively to that of the arm. Using the same method as before we see that while d is carried forward through co by the

action of the arm, it is caused to turn co x =-3 in the opposite

o ct

direction as a is moved back to its original place, so that the actual total angular motion of d is :