SCREW. This mechanical power generally consists of two parts, one of which is a solid cylinder of wood or metal, on whose convex surface is formed a projecting rib ur fillet, frequently called a thread, which passes spirally round in such a manner as constantly to make equal angles with lines parallel to the axis of the cylinder. The other is a cylindrical perforation through a block of some material, the surface of the perforation having on it a spiral groove correspond ing to the projecting rib or fillet on the solid cylinder. The first of these parts is called a eon= screw, and the other a concave screw, also a male and frauds screw.
A just conception of the nature of the line of direction taken by the rib or groove on the surface of the cylinder, may be obtained' by drawing on a rectangular paper, whose breadth A B is equal to the cir cumference of ,the cylinder, any number of lines B, D, El, equidistant from each other, and perpendicular to the sides of the paper. Then joining the points A and n, C and F, &c., by right lines, and bending the paper on the surface of the cylinder, the lines A D, C F, E &c., will, by uniting at their extremities, become the con tinuous helix or spiral curve-line which the thread assumes. When the two parts are in action, the convex screw, being turned round in the other by a power applied at its surface, moves at the same time rectilinearly in the direction of its axis : occasionally however the convex screw is fixed, and then the other being turned about, it acquires at the same time a like rectilinear motion. In either case, the path described by a point on any thread during the time that the screw turns once on its axis, on being developed, becomes equal to A n or o F; and in the same time a point on the axis moves through a apace equal to B D or D F.
As a mechanical power, the screw possesses the properties of an inclined plane; for w representing a weight or pressure at one end of a convex screw, whose threads are thereby made to move in the grooves of the concave screw, let that weight be supposed to act in a direction parallel to the axis, and to be uniformly diffused among all the projecting threads which are at one time in the grooves ; also let p be the part of the weight which presses in the direction mat on an elementary portion un of the side of a groove in the concave screw.
Then sin may be considered as a small inclined plane, making with VIM an angle equal to A D n : and if q be a force which applied at II in the direction N it, touching a circle whose plane passes through the screw perpendicularly to the axis, would prevent the convex screw from turning round ; the pressure on stn and the counteracting force will be in the same circumstances as the weight of any body on an inclined plane and a sustaining power which acts iu a direction parallel to the base of a plane, and, by the resolution of forces, the ratio between the pressure and the force will be as the base of the plane is to its height; that is, as A B to an. Now an equal force q will be in equilibrio with the pressure p on every other elementary portion of the grooves in the concave screw; therefore, there being as many forces= q as there are pressures=p, the whole weight w on the screw will be to the whole sustaining force, in the case of equilibrium as A B to B D ; that ia, as the circumference of the convex screw is to the distance between the threads when measured in a direction parallel to the axis.
But the screw, when applied as a mechanical power, is never used in its simple state; a lever or wheel is always fixed perpendicularly to the axis, and the moving or sustaining power is applied near the outer extremity of the lever, or at the circumference of the wheel. In this last case, the ratio between the moving-power and the resistance is as the distance between the threads of the screw is to the length of that circumference ; and the velocity of a point on the axis is to that of a point on the circumference in the same ratio. The friction of a screw is however very great, and is frequently equal to, at least, the weight supported, for it will prevent that weight from descending when the moving-power is taken away.