COUPLINGS.] 



APPLIED MECHANICS. 



883 



vibration effected in a second, and that the arc described 

 by A measures 2 feet in length, then will the arc de- 

 scribed by C be 1 foot long ; and 10 Ibs. at A, moving 

 through 2 feet in 1 second, develops the same power as 

 20 Ibs. at C moving through 1 foot in 1 second, because 

 10 X 2=20 X 1 ; the products of the pressures by the 

 velocities ar equal in both cases. We might trace the 

 same law through all the simple mechanical powers, and 

 through all possible combinations of them ; that is to say, 

 through all possible arrangements of machinery. 



The practical application of this law in calculating the 

 proper strengths and proportions of parts of machines, is 

 exceedingly simple. 



In a machine, for instance, moved by 1 horse-power, 

 whenever we can ascertain the velocity of any part, we 

 can find at once the pressure or strain passing through 

 that part. One-horse power is reckoned as 33,000 Ibs. 

 moved 1 foot per minute ; if, then, some part of the 

 machine in question were found to move over 10 feet in 

 1 second, or 600 feet in 1 minute, we should at once 

 know that the strain on that part is equivalent to a 

 pressure of 65 Ibs., for 55 Ibs. X 600 feet =33000 Ibs. X 1 

 foot. As a practical example, let us suppose that in 

 some part of a machine worked by 5 horse- 

 power, there is a wheel 7 feet in diameter, 

 revolving 30 times in a minute, and that 

 re to estimate the pressure on the 

 rim of that wheel, or the resisting force 

 which ould have to be applied to balance 

 ita rotary force. 



The circumference of a wheel 7 feet in 

 diameter is 22 feet, and this moving 30 

 times round in a minute, has a velocity of 

 22 x 30=660 feet per minute ; the power, 

 5-horse, is equivalent to 33000 x 5 = 

 165000 Ibs. moved through 1 foot per 

 minute, or 250 Ibs. moved through C60 

 feet per minute. The strain on the rim of the wheel 

 is therefore equivalent to 250 Ibs. Generally, the 

 rule for estimating the strain (in Ibs.) of any part, is to 

 divide the power (expressed in Ibs. moved over 1 foot per 

 minute) by the velocity of the part (in feet per minute). 

 ROTARY MOTION. The kind of motion most con- 

 veniently conveyed through machinery is rotary motion ; 

 and the chief subject of our enquiry will be as to how this 

 can be conveyed and converted into motions of another 

 kind, such as vibratory or reciprocating movements. 



A shaft or spindle is a rigid bar of metal, or sometimes 

 of wood, caused to rotate round its axis, and capable of 

 conveying the rotary motion given to it along its whole 

 length, and giving it off at any point to machinery con- 

 nected with it. The lengths of shafts are limited in con- 

 sequence of the difficulties attending their construction 

 in great lengths. Large shafts, such as are used for the 

 paddles of marine engines, are sometimes 20 or 30 feet 



D E, made slightly taper, and driven tightly in from 

 each end. One of the shafts A being caused to rotate, 

 must carry the coupling C round with it, and also the 

 other shaft B, because the keys prevent either shaft from 

 slipping round within the coupling, or the couplfng from 

 slipping round either. In making such a coupliug of 

 cast-iron, the following proportions will be found prac- 

 tically suitable : External diameter of coupling double 

 that of shaft ; length of coupling three times the diameter 

 shaft ; width of key, one-fourth the diameter of shaft ; 

 mean depth of key, one-half its width. 



The keys should be made with gib-heads, as shown in 

 the figure, so that they may be driven out when required, 

 by applying a piece of iron rod to the projecting part and 

 striking it with a hammer, as marked by the dotted lines 

 F, or by driving a wedge between the gib-head and the 

 coupling. * 



Some engineers, in coupling the shafts, halve them over 

 each other, as in Fig. 214, and insert a tapered key in a 

 groove formed in the coupling only, its inner surface 

 fitting the shafts. Such a key, called technically a Itollow 

 key, from the hollowing or concavity of its inner surface, 

 Kg. 211. 



tightens the coupling very firmly on the shafts. The 

 fcux-cmipling (Fig. 215) consists of two discs, with pro- 

 jecting bosses keyed on the ends of the shafts facing each 

 other, held together by four or more bolts and nuts pass- 

 ing through corresponding holes in the two discs. 



Sometimes, when it is desired that by no accident shall 

 the movement of any length of shafting be reversed, a 

 ratchet-coupling is applied, a (Fig. 216) is a toothed 

 boss, keyed firmly on the shaft d, and b a similar 

 toothed boss capable of sliding longitudinally on the 

 shaft c along a feather or parallel key, wliich prevents 

 it from turning round independently of c. So long 

 as the shaft d revolves in one direction, it carries 

 the other shaft c round with it ; but should the ro- 

 tation of d be reversed, the pressure on the inclined 

 faces of the teeth causes the boss 6 to slip out of gear 

 with o, and thus to uncouple the two shafts. 



CLUTCH. When it is desired to couple or uncouple 

 Fig. 213. 



\ \ f 



long; but smaller shafts seldom exceed 10 or 12 feet 

 in length. When greater lengths are required, the 

 shafts have to be coupled or connected together. 



COUPLINGS. Fig. 213 represents a simple coupling 

 for round wrought- iron shafts. A and B, the ends of the 

 two shafts, being nicely rounded, are inserted into a cylin- 

 drical box C bored to fit them, and having a groove or key- 

 way cut along its interior surface, corresponding to grooves 

 cut in the shafts. These grooves are filled by keys, 



two lengths of shafting at pleasure, a clutch, like that 

 represented in Fig. 217, is generally employed. 



A, the driving shaft, on which is keyed firmly a half 



A *' key," used for fixing a coupling or any other piece of machinery 

 on a round shaft, is a piece of iron or steel of parallel breadth, but 

 slightly tapered in thickness, so that on driving it into the " key-way" or 

 recess provided for it, it acts as a wedge, pressing the opposite surface of 

 the shaft against that of the hole. A " feather" is a key of equal breadth 

 and thickness throughout, fitted into a recess in the shaft, and projecting 

 from it into a slot formed in the hole of the coupling or other boss, which 

 can thus elide along the shaft longitudinally, but must turn with it. 



