The first two cases are exemplified in the different forms which are given to the common press, and the last case is exemplified in the construction of the self-acting slide rest of the lathe, and in other kinds of mechanism.

The screw is usually employed for producing very slow uniform motions, and for exerting great pressure through a limited space.

The Common Press.

Fig.75.

104. In fig. 75, s s is the solid screw, N the nut, N P the lever, B the lower press-board which is constrained to move in an upward direction by means of the guide-frame.

Case 1.-In this case the nut N revolves, but does not move longitudinally, but the screw ss is incapable of revolving. Hence the press-board B is moved upwards at every revolution of the nut over a space equal to the pitch of the screw, or the distance between the threads; that is,

100

lever N P = 2 ft.; required the velocity ratio of the point P and the press-board B.

velo. P 2 × 2 × 12 × 3·1416

velo. B

=

=753.984;

that is, the velocity of P is 753.984 times that of B.

Case 2.-In this case N is a perforated cylinder forming part of the solid screw s s, and therefore turns with it on a pivot which works in a socket placed on the under side of the press-board B; the piece K fixed to the frame contains the hollow or female screw; so that the solid screw s s is capable of revolving and of moving longitudinally, whilst the nut K remains absolutely fixed.

Fig. 76,

Compound Screw.

105. This mechanism consists of two screws A and D, the smaller one D working within the larger one A.The screw A works in a fixed nut or female screw at K, and is capable of revolving and moving in the direction of its length; the small screw D is incapable of revolving, but is capable of moving in the direction of its length. In one revolution of the lever P, the screw a descends a space equal to the distance between its threads, but at the same time the screw D enters the hollow screw formed in A a space equal to the distance between the threads on D, so that the extremity B will only descend a space equal to the difference between the thickness of the threads on A and the thickness of the threads on B; hence we have

circum. described by P

dist. bet. threads on A dist. bet. threads on D.

If the length of the lever P = r, the pitch of the screw a = t, and the pitch of D =

t1; then

The same velocity ratio might be attained by making the pitch of a single screw a equal to t

t,, but the threads, in this case, might be too weak to stand the pressure; hence the advantage of the compound screw.

The Endless Screw.

A

Fig. 77.

106. When the threads or teeth of a revolving screw are made to act upon the teeth of a wheel, as in fig. 77, the mechanism is called the endless screw. Here, each rotation of the axis A B of the screw turns round one tooth of the wheel c, the pitch of the screw on the axis A B being equal to the pitch of the teeth on the wheel.

If q and q be the synchronal rotations of the wheels and the screw respectively, and N the number of teeth in the wheel; then

B

formed by the wheel the screw will make 40.

If R, r be the respective pitch-radii of the wheel and screw, being, as before, the angle which the thread of the screw makes with its axis; then

107. A D is an axis on which are formed two screws, A B and BC, whose pitches are differ

Fig. 78.

capable of moving longitu

dinally, but incapable of revolving from the interven

tion of the guides.

Let the screw make one turn so as to move the cylinder from

right to left, then the screw A B will move through the fixed nut E a space equal to the distance between its threads; but, at the same time, the screw B C will move through the nut Na space equal to the thickness of the threads on B C; so that the nut N will only be moved through a space equal to the difference between the thickness of the threads on A B and B c; that is— In one revolution of A, the space moved over by the nut N= pitch screw A B-pitch screw B C t-t1, where t is put for the pitch of the screw A B, and t, for that of B C.

If t=

t,, then nut N will remain at rest.

If the screw A B be right-handed, and B c left-handed, then t + t1 will be the space moved over by the nut N in one revolution of A.

The Archimedian Screw Creeper.

108. This machine is used for conveying corn from one part of a corn-mill to another. It consists of a wooden cylindrical trough, A B C D, with which revolves a shaft, E F, having a deep

spiral thread formed upon its surface. The corn is dropped in at one extremity of the trough by a hopper, and by the revolution of the creeper the corn is pushed along towards the other extremity of the trough.

Mechanism for Cutting Screws.

109. C D is the cylinder or axis on which the screw is to be cut, revolving with the mandril D of the lathe; A a toothed wheel revolving with the axis C D, and giving motion to the toothed wheel B, round its axis F E, on which is cut the parent

screw; this screw gives a longitudinal motion to the nut N, as in Case 3, carrying the sliding table or saddle upon which is securely clamped the cutting tool P intended to cut the thread of the screw on the cylinder c D. In the place of the wheels a B, any combination of wheels may be used so as to produce any relative longitudinal velocity to the cutting tool P, and thereby to form a screw of any given pitch on C D with the same parent

Let n the no. teeth on the wheel A, n1 = the no. teeth on B, t= the pitch of the screw on C D, t1 = the pitch of the screw on FE; then

which expresses the pitch of the screw on C D.

From this equality we get

that is to say, the pitches of the screws are in the ratio of the number of teeth on their respective wheels.

If n, and t1 be constant, then

t∞on;