Screw. Under ROTATION it is pointed out that the most general displacement which a rigid body can experience may be represented by a screw motion about and along a definite axis. The kinematic characteristic of screw motion is easily studied by help of any ordinary screw working in its nut. We may fix the nut and consider the motion of the screw; or fix the screw and consider the motion of the nut. In either case we find a certain translation associated with a proportional amount of rotation. The ratio of the translation to the associated rotation is called the pitch of the screw. In an ordinary single-threaded screw the practical measure of the pitch is the distance between the threads, and is simply the translation for one complete rotation. In dynamics it is more scientific to take the pitch as the translation for a rotation through the radian or unit angle (see CIRCLE). The ratio of the scientific to the practical pitch is the same as the ratio of the circumference of a circle to its radius. The smaller the pitch, the less is the translatory motion for a given rotation; and when the pitch is made zero, the screw motion is reduced to a pure rotation. On the other hand, the larger the pitch, the greater is the translation for a given rotation; so that a screw of infinite pitch corresponds to a pure translation. Thus screw motion includes all possible kinds of motion, translation and rotation being limiting cases.
Dynamically, screw motion is said to be produced by a wrench, which is the most general quantity of the force type. When the screw motion is reduced to translation, the wrench becomes force in the usual sense of the word; and couple, which produces rotation, is the other limiting case of wrench. The simplest conception of a wrench is obtained from the combination of pushing and twisting needed to bore holes with a gimlet.
The screw is a very important element in machinery. In itself, however, it is not complete, being only half of the screw-pair or elementary mechanism to which it belongs. The complete mechanism is well illustrated by the combination of screw and nut. By making the pitch zero, we pass to the one limiting case known as the turning-pair; and by making the pitch infinite we get the other limiting case—viz. the sliding-pair. These three combinations form the simple elements of all machines.
One of the most important uses of the screw (as in the screw-press) is to apply or sustain a large pressure in the direction of its axis by means of a comparatively small couple acting about its axis. We shall suppose the couple to be applied by a force, , acting at the end of a lever attached to the screw; and that the result is a thrust, . If is the arm of the lever, and the pitch, the principle of work (see ENERGY) gives us the relation . Hence the smaller the pitch the greater the pressure exerted by the screw for a given couple acting round its axis. The pitch is diminished by making the thread of the screw finer. But, as this also makes it weaker, we see that there must be a practical limit to increasing the advantage of the screw in this way. So far we have neglected friction, which must, however, be considerable in all screw-pairs because of the great pressures existing between the opposed faces of the threads of the screw and nut. The power applied, , must, therefore, be greater than the effective work done. In some cases, when the pitch is small, the efficiency, or ratio of useful work done to work expended, may be reduced to one-third. If the pitch is very large the action of the screw may be reversed, the driving force being the thrust, , and the resistance the couple, , opposing the rotation of the screw. In most cases the pitch is too small for reversal, the couple brought into play by the friction always being sufficient to prevent motion. It is this non-reversibility that gives the screw its peculiar virtue in holding together parts of a frame or machine. For the screw-propeller, see SHIPS AND SHIPBUILDING.