THE EPICYCLOIDAL PULLEY-BLOCK.
223. We shall conclude this lecture with some experiments upon a useful mechanical power introduced by Mr. Eade under the name of the epicycloidal pulley-block. It is shown in [Fig. 33], and also in [Fig. 49]. In this machine there are two chains: one a slight endless chain to which the power is applied; the other a stout chain which has a hook at each end, from either of which the load may be suspended. Each of these chains passes over a sheave in the block: these sheaves are connected by an ingenious piece of mechanism which we need not here describe. This mechanism is so contrived that, when the power causes the sheave to revolve over which the slight chain passes, the sheave which carries the large chain is also made to revolve, but very slowly.
224. By actual trial it is ascertained that the power must be exerted through twelve feet and a half in order to raise the load one foot; the velocity ratio of the machine is therefore 12·5.
225. If the machine were frictionless, its mechanical efficiency would be of course equal to its velocity ratio; owing to the presence of friction the mechanical efficiency is less than the velocity ratio, and it will be necessary to make experiments to determine the exact value. I attach to the load hook a weight of 280 lbs., and insert a few small hooks into the links of the power chain in order to receive weights: 56 lbs. is sufficient to produce motion, hence the mechanical efficiency is 5. Had there been no friction a power of 56 lbs. would have been capable of overcoming a load of 12·5 × 56 = 700 lbs. Thus 700 units of energy must be applied to the machine in order to perform 280 units of work. In other words, only 40 per cent. of the applied energy is utilized.
226. An extended series of experiments upon the epicycloidal pulley-block is recorded in Table XII.
Table XII.—The Epicycloidal Pulley-Block.
Size adapted for lifting weights up to 5 cwt.; velocity ratio 12·5; mechanical efficiency 5; useful effect 40 per cent.; calculated formula P = 5·8 + 0·185 R.
| Number of Experiment. | R. Load in lbs. | Observed power in lbs. | P. Calculated power in lbs.. | Differences of the observed and calculated powers. |
|---|---|---|---|---|
| 1 | 56 | 15 | 16·2 | +1·2 |
| 2 | 112 | 27 | 26·5 | -0·5 |
| 3 | 168 | 40 | 36·9 | -3·1 |
| 4 | 224 | 47 | 47·2 | +0·2 |
| 5 | 280 | 56 | 57·6 | +1·6 |
| 6 | 336 | 66 | 68·0 | +2·0 |
| 7 | 392 | 78 | 78·3 | +0·3 |
| 8 | 448 | 88 | 88·6 | +0·6 |
| 9 | 504 | 100 | 99·0 | -1·0 |
| 10 | 560 | 110 | 109·4 | -0·6 |
The fourth column shows the calculated values of the powers derived from the formula. It will be seen by the last column that the formula represents the experiments with but little error.
227. Since 60 per cent. of energy is consumed by friction, this machine, like the differential pulley-block, sustains its load when the chains are free. The differential pulley-block gives a mechanical efficiency of 6, while the epicycloidal pulley-block has only a mechanical efficiency of 5, and so far the former machine has the advantage; on the other hand, that the epicycloidal pulley contains but one block, and that its lifting chain has two hooks, are practical conveniences strongly in its favour.
LECTURE VIII.
THE LEVER.
The Lever of the First Order.—The Lever of the Second Order.—The Shears.—The Lever of the Third Order.