A Treatise on the Theory of Screws

52] THE REPRESENTATION OF THE CYLINDROID BY A CIRCLE. 47 screw, and the line PT may be called the axis of pitch. We have, accord- ingly, the following theorem :— The pitch of any screw on the cylindroid is equal to the perpendicular let fall on the axis of pitch from the corresponding point on the circle. A parallel AA' to the axis of pitch cuts the circle in two points, A and A', which have equal pitch. The diameter perpendicular to the pitch axis intersects the circle in the points U, V of maximum and minimum pitch. These points, of course, correspond to the two principal screws on the cylin- droid. The two screws of zero pitch are defined by the two real or imaginary points in which the axis of pitch cuts the circle. A fundamental law of the pitch distribution on the several screws of a cylindroid is simply illustrated by this geometrical representation. The law states that if all the pitches be augmented by a constant addition, the pitches so modified will still be a possible distribution. So far as the cylindroid is concerned, such a change would only mean a transference of the axis of pitch to some other parallel position. The diameter 2m merely expresses the size of the cylindroid, and is, of course, independent of the constant part in the expression of the pitch, 52. The Distance between two Screws. We shall often find it convenient to refer to a screw as simply equivalent to its corresponding point on the circle. Thus, in fig. C, the two points, A and B, may conveniently be called the screws A and B. The propriety of this language will be admitted when it is found that everything about a