motion normal to the screw line must be impossible. With this object various forms are given in the common screw to the section perpendicular to the direction of sliding, all being formed so that the sectional profile is double sided, as in the various forms shown in the annexed figure.
Fig. 39.
In a closed pair having a profile such as the foregoing every motion oblique to the helix is rendered impossible, so that only motion along the helix itself can take place. Everyone is familiar with the use of these profiles in the ordinary screws employed in construction. If a straight line parallel to the axis and longer than the pitch of the screw be used to generate a screw surface, the surface obtained coincides with that of a circular cylinder, so that in a pair of bodies formed of screw surfaces of this kind only relative radial motion would be prevented, they would not be constrained so far as motion in any other direction is concerned.
We may now proceed to examine more closely the effect of altering the two essential dimensions of the closed pair which we have found, a screw and nut having a thread of suitable profile. Any such screw owes its special properties to two quantities, its radius or circumference and its pitch-angle, (or angle which has for its tangent the ratio pitch: circumference).
The alteration of the radius alone, (the pitch-angle remaining constant), gives us no new form, all the properties of the original screw remain unchanged.
With the angle of pitch it is otherwise. If this be gradually diminished, the diameter remaining constant, the pitch becomes less and less, until at last if the angle be reduced to zero the pitch disappears altogether; the profile has a motion of rotation only, and describes simply a solid of revolution. The profile- section, however, in a plane at right angles to the direction of sliding remains unaltered, and has become the form by which
