| Pa | the axial | pitch |
| Pa/n = pa | divided pitch; | |
| Pn | the normal | pitch |
| Pn/n = pn | divided pitch; | |
| Pc the circumferential pitch; | ||
then
| pc = pa cot θ = pn cos θ = | 2πr | , |
| n |
| pa = pn sec θ = pc tan θ = | 2πr tan θ | , |
| n |
| pn = pc sin θ = pa cos θ = | 2πr sin θ | . |
| n |
(31)
If a screw rotates, the number of threads which pass a fixed point in one revolution is the number of threads in the screw.
A pair of convex screws, each rotating about its axis, are used as an elementary combination to transmit motion by the sliding contact of their threads. Such screws are commonly called endless screws. At the point of contact of the screws their threads must be parallel; and their line of connexion is the common perpendicular to the acting surfaces of the threads at their point of contact. Hence the following principles:—
I. If the screws are both right-handed or both left-handed, the angle between the directions of their axes is the sum of their obliquities; if one is right-handed and the other left-handed, that angle is the difference of their obliquities.
II. The normal pitch for a screw of one thread, and the normal divided pitch for a screw of more than one thread, must be the same in each screw.