SCREW-CUTTING GEAR.] 



APPLIED MECHANICS. 



897 



SCREW-CUTTING GEAR. It is often required to 

 change a rectilineal motion, having a certain velocity, to 

 Fig. 260, 



one having another velocity, particularly in machinery 

 for cutting screws. A screw, as we have already de- 

 scribed, is a line traced on the surface of a cylinder by 

 the motion of a point moving longitudinally along the 

 cylinder, parallel to its axis, while the cylinder revolves. 

 The pitch of the screw is the distance through which the 

 tracing point moves longitudinally while the cylinder 

 makes one revolution ; and in practice, it is necessary to 

 form screws of numerous different pitches, according to 

 tlieir dimensions, and the circumstances under which 

 they are to be used. The pitch of a screw is generally 

 named according to the number of turns or convolutions 

 which the screw makes in a certain length of the cylinder. 

 Thus, when a screw has 8 turns to the inch, we say that 

 it has a pitch of Jth of an inch that is, during one re- 

 Fig. 261. 



volution of the cylinder on which the screw is formed, 

 the tracing point advances longitudinally Jth of an inch, 

 or while the tracing point advances 1 inch, the cylinder 

 revolves 8 times. 



A (Fig. 261) is a cylinder revolving in bearings at each 

 end, with a toothed wheel B fixed at one end, and D a 

 screw mounted in bearings parallel to the cylinder, and 

 carrying a nut F, with a tracing point G projecting from 

 it, to meet the surface of the cylinder, the screw having 

 a toothed wheel E, gearing into an intermediate wheel 

 C, which also gears into B. On causing the cylinder A 

 to revolve, the screw D is also caused to revolve ; the nut 

 F and tracer G are made to move longitudinally parallel 

 to the axis of A, and the screw-curve traced on A is that 

 due to the velocity with which A revolves, as compared 

 to the speed with which G advances. By altering the 

 proportions or numbers of teeth in the wheels B and E, 

 the relative velocities of the cylinder and screw may be 

 changed at pleasure, and the pitch of the screw traced on 

 A from a screw D of constant pitch may be proportionally 



VOL. I. 



varied. In lathes, or machines for cutting screws, the 

 cylinder A is the piece of metal on which the screw is to 

 be cut ; its axis is what is technically called the mandril of 

 the lathe ; and the tracing point G is a steel tool cutting 

 into the metal, so as to leave the screw-thread projecting. 

 The screw D has generally a pitch which is some simple 

 fraction of an inch, such as or Jrd of an inch, and the 

 lathe is furnished with numerous toothed wheels, which 

 may be put in the place of B and E to vary the pitch of 

 the cut-screw, as may be required. If we take the case 

 of a lathe having a screw D of i an inch pitch, or making 

 2 turns per inch, when the wheels B and E have equal 

 numbers of teeth, whatever be the size of the interme- 

 diate wheel C, the screw D revolves with the same 

 angular velocity, and in the same direction with the 

 work A. The tool G, therefore, advances ^ an inch 

 along the surface of A during each revolution of A, and 

 cuts a screw of precisely the same pitch, and lying in the 

 same direction with that on the screw D. But if in 

 place of two equal wheels B and E, we put wheels, B 

 having 20 teeth, and E having 40, then the screw D will 

 be caused to revolve at jgths, or | the speed of A, and the 

 tool will advance i of ^ an inch, or Jth of an inch, during 

 each revolution of A, and thus to cut a thread of Jth of 

 an inch pitch upon it. Screw-cutting lathes are generally 

 furnished with a table of screw pitches, and the appropriate 

 wheels for producing them, such, that the workman, by 

 inspecting the table, can at once select the proper wheels 

 for giving the desired pitch. The wheels belonging to 

 the lathe have their numbers of teeth stamped upon 

 them, to save the trouble of counting them. Sometimes, 

 when the difference of the speed of the screw and of the 

 work is required to be considerable, instead of the simple 

 intermediate wheel C, it is necessary to introduce a 

 wheel and pinion C and c fixed together. Thus, if it 

 were required that the screw should revolve at J 5 th of the 

 velocity of the mandril, were the smallest possible 

 wheel B to have 20 teeth, it would be necessary that E 

 should have 500 teeth, because -gfo = -jVth, if the simple 

 intermediate wheel C were employed. This size of wheel 

 for E might be extremely inconvenient, and it would be 

 better to employ the compound intermediate wheel and 

 pinion C and c. In this arrangement, B having 20 teeth, 



C 100, c 20, and E 100, the speed of E is 



20 X 20 

 100 X 100 



= /jth of that of B. In the lathe table, the first 

 column gives the pitch of the screw to be cut ; the second 

 gives the number of teeth on the mandril wheel B ; the 

 third and fourth give the numbers of teeth in the 

 intermediate wheels C and c respectively ; and the 

 fifth gives the number on the screw-wheel E. When 

 the compound intermediate wheels are not required, 

 the columns of intermediates are left blank, as any 

 simple intermediate may be employed without altering 

 the relative velocities of the mandril and screw-wheels. 

 ^ I The following is part of a table for a lathe having a 

 screw of inch pitch : 



TABLE OF SCREW GEARING FOR LATHE. 



CY 



