Pinion. In general, the smaller of two gears meshing together, but in particular the one that is driven; we use it in the latter sense in all articles concerning pinions , especially the article Tooth, where in everything we say about the shape of wheel teeth and pinion leaves it should be understood that the wheel drives and the pinion is driven. Machinery employs two types of pinion ; heavy machines usually have lantern pinions (Figure 5, NY) [1], and in lighter machines pinions with teeth or leaves arranged and shaped in about the same way as wheel teeth, in watches, clocks, etc.

The trundles, AB, of lantern pinions are usually cylindrical. Several craftsmen have lately revived the old practice of having the trundles turn on their axes, among them M. Harrison, in his first longitude clock; the goal is reducing the friction of the wheel teeth on the trundles, but although this friction is worth taking into consideration, it is not the essential factor in a gear set. It is the uniformity of the wheel's action on the trundle or leaf of the pinion , as has been seen in the article Tooth, a uniformity that is difficult to obtain when the trundles turn on their axes; they must be of a certain thickness, or the advantage would be almost nil, and this makes it difficult to give the tooth the shape required for it always to drive the trundle uniformly.

M. de la Hire, in his Traité des épicycloïdes , demonstrates that for a tooth to drive the trundle with constant uniformity, assuming the latter is infinitely slender, the shape of the tooth must be the portion of an epicycloid generated by a circle having the diameter of the pinion and rolling on the circumference of the wheel. See [Plate XVI, key SS] Figure 101, of Gearing. [2] But since such a trundle does not exist and they all have a certain diameter, he goes on to say that to compensate, the epicycloid just mentioned having been described, from all its points on its concave side small arcs must be drawn with a radius equal to that of the trundle; the intersection of all those arcs will form a new curve, which will be the one required. As for ordinary pinions , used in watches and clocks, the faces of their leaves or teeth must complete a straight line from the center, as we have seen in the article Tooth. See the pinion in Figure 102.

In general, the shape of pinion leaves must always be determined by that of the wheel teeth, but since there are tooth shapes for which it would be impossible to devise one for the pinion leaves resulting in the uniform motion of the pinion , and moreover since it would often be impractical to give the leaves certain required shapes, the plane surface has been chosen as the simplest and the easiest to make.

For a pinion to be correctly made, it must be well polished, the faces of the leaves must align with the center, and the axis must be the meeting point of their planes.

The relation of pinion diameters to that of the wheels with which they mesh must be as the number of their leaves is to the teeth in the latter, so it follows that the teeth of each are always equal, in other words that the chord of a pinion tooth must equal that of a wheel tooth. Now for clocks and watches the wheels are usually made first, and their diameters determine those of the pinions ; therefore any number of wheel teeth taken for the diameter of the pinion , according to the analogy: 7 is to 22 as the teeth of the wheel are to the number sought, the fourth term will be the number of the pinion . When that number is given, by reversing the analogy: 22 is to 7 as the number of the pinion is to the number sought, one obtains the number of wheel teeth to be used for the diameter of the pinion . Horologists often argue about the true diameter of pinions and the method for finding it, but that is because they do not understand what is at issue; once the numbers of a meshing pinion and wheel are given, as well as the diameter of the wheel, the diameter of the pinion is also known without fail, and it cannot be more or less than a certain size, since the two diameters must be to each other as the numbers of the pinion and the wheel. The only difficulty would concern that surplus part of the pinion and wheel teeth that is rounded, but once the true diameters of both are determined, that is easy to find because the pinion must be rounded only if its face angles are too sharp.

Pinion, intermediate. A pinion used to relay motion from one part of the clock to another, as from the movement to the motion work, etc.

Pinion, fan. In the strike or repetition train, the last pinion in the train, also called the "governor." It is called the fan pinion because in tall-case and bracket clocks, and sometimes in watches, it has on its arbor a part called a fan . See Fan, Strike, etc.

1. Illustration not found.

2. Plate incorrectly labeled "Horology tools."