To obtain the forms of the teeth, therefore, take any convenient describing circle, and employ it to describe the teeth of the pinion by rolling within its pitch circle, and to describe the teeth of the wheel by rolling within and without its pitch circle, and the pinion will then work truly with the teeth of the wheel in both positions. The tooth at each extremity of the series must be a circular one, whose centre lies on the pitch line and whose diameter is equal to half the pitch.
Fig. 213.
If the reciprocating piece move in a straight line, as it very often does, then the mangle-wheel is transformed into a mangle-rack ([Fig. 213]) and its teeth may be simply made cylindrical pins, which those of the mangle-wheel do not admit of on correct principle. b b is the sliding piece, and a the driving pinion, whose axis must have the power of shifting from a to a through a space equal to its own diameter, to allow of the change from one side of the rack to the other at each extremity of the motion. The teeth of the mangle-rack may receive any of the forms which are given to common rack-teeth, if the arrangement be derived from either [Fig. 210] or [Fig. 211].
But the mangle-rack admits of an arrangement by which the shifting motion of the driving pinion, which is often inconvenient, may be dispensed with.
Fig. 214.
b b [Fig. 214], is the piece which receives the reciprocating motion, and which may be either guided between rollers, as shown, or in any other usual way; a the driving pinion, whose axis of motion is fixed; the mangle rack c c is formed upon a separate plate, and in this example has the teeth upon the inside of the projecting ridge which borders it, and the guide-groove formed within the ring of teeth, similar to [Fig. 211].