Now suppose that the wheels had been rotated in the opposite direction and the same form of curve would be produced, but it would run in the opposite direction, and these two curves may be utilized to form teeth, as in [Fig. 22], the points on the wheel a working against the curved sides of the teeth on b.
Fig. 23.
To render such a pair of wheels useful in practice, all that is necessary is to diminish the teeth on b without altering the nature of the curves, and increase the diameter of the points on a, making them into rungs or pins, thus forming the wheels into what is termed a wheel and lantern, which are illustrated in [Fig. 23].
a represents the pinion (or lantern), and b the wheel, and c, c, the primitive teeth reduced in thickness to receive the pins on a. This reduction we may make by setting a pair of compasses to the radius of the rung and describing half-circles at the bottom of the spaces in b. We may then set a pair of compasses to the curve of c, and mark off the faces of the teeth of b to meet the half-circles at the pitch line, and reduce the teeth heights so as to leave the points of the proper thickness; having in this operation maintained the same epicycloidal curves, but brought them closer together and made them shorter. It is obvious, however, that such a method of communicating rotary motion is unsuited to the transmission of much power; because of the weakness of, and small amount of wearing surface on, the points or rungs in a.
Fig. 24.
In place of points or rungs we may have radial lines, these lines, representing the surfaces of ribs, set equidistant on the radial face of the pinion, as in [Fig. 24]. To determine the epicycloidal curves for the faces of teeth to work with these radial lines, we may take a generating circle c, of half the diameter of a, and cause it to roll in contact with the internal circumference of a, and a tracing point fixed in the circumference of c will draw the radial lines shown upon a. The circumstances will not be altered if we suppose the three circles, a, b, c, to be movable about their fixed centres, and let their centres be in a straight line; and if, under these circumstances, we suppose rotation to be imparted to the three circles, through frictional contact of their perimeters, a tracing point on the circumference of c would trace the epicycloids shown upon b and the radial lines shown upon a, evidencing the capability of one to impart uniform rotary motion to the other.