But a floor, however heavy, suspended by three wire ropes and properly balanced over large, well-mounted pulleys, requires an amount of energy to work it which does not exceed that required to operate a platform of moderate dimensions, and there is a freedom, a safety and a facility of working with a complete floor which no partial platform can give.
The Torque Was Measured By Weights 0 And P Suspended By Silk Ribbons Passing Over The Pulleys N And Round The Disk Kl.
Suppose the base-circles to be a pair of circular pulleys connected D~ ill by means of a cord whose course ~f from pulley to pulley is P1IP2.
As the line of connection of those pulleys is the same as that of the I proposed teeth, they will rotate -
Wrapping ConnectorsBelts, Cords and Chains Flat belts of leather or of gutta percha, round cords of catgut, hemp or other material, and metal chains are used as wrapping connectors to transmit rotatory motion between pairs of pulleys and drums.
Chains require pulleys or drums, grooved, notched and toothed, so as to fit the links of the chain.
Pulleys and drums for communi cating a constant velocity ratio are circular.
The angular velocities of a pair of connected circular pulleys or drums are inversely as the effective radii.
The length L of an endless belt connecting a pair of pulleys whose effective radii are r,, r,, with parallel axes whose distance apart is c, is given by the following formulae, in each of which the first term, containing the radical, expresses the length of the straight parts of the belt, and the remainder of the formula the length of the curved parts.
When the a,ces of a pair of pulleys are not parallel, the pulleys should be so placed that the part of the belt which is approaching each pulley shall be in the plane of the pulley.
The speed-cones are either continuous cones or conoids, as A, B, whose velocity ratio can be varied gradually while they are in motion by shifting the belt, or sets of pulleys whose radii vary by steps, as C, D, in which case the velocity ratio can be changed by shifting the belt from one pair of pulleys to another.
One train of mechanism may diverge into two or moreas when a single shaft, driven by a prime mover, carries several pulleys, each of which drives a different machine.
F = T1 Ti = T1 (I ef9) Ta(ef 1)j When a belt connecting a pair of pulleys has the tensions of its two sides originally equal, the pulleys being at rest, and when the pulleys are next set in motion, so that one of them drives the other by means of the belt, it is found that the advancing side of the belt is exactly as much tightened as the returning side is slackened, so that the mean tension remains unchanged.
Trans., 1894) investigated the question for the cases of loaded and unloaded shafts, and, owing to the complication arising from the application of the general theory to the cases of loaded shafts, devised empirical formulae for the critical speeds of shafts loaded with heavy pulleys, based generally upon the following assumption, which is stated for the case of a shaft carrying one pulley: If Ni, N1 be the separate speeds of whirl of the shaft and pulley on the assumption that the effect of one is neglected when that of the other is under consideration, then the resulting speed of whirl due to both causes combined may be taken to be of the form N1N2~!
This form is extended to include the cases of several pulleys on the same sifaft.
Such persons may sometimes get a good deal of exercise in a short time by the use of dumb-bells, of elastic cords, or of cords running over pulleys and weighted at one end.
These wheels receive motions from bands and pulleys from a steam or other engine contained in the car.
Thus these two small pulleys are always running, but in opposite directions.
When the poise is at the zero end, and there is no load on the platform, the end of the steelyard is down, and has locked the ratchet wheel by means of the pawl; the shaft being thus locked, the sprocket wheels are stopped, the drum-shaft runs free by the friction clutch, and the two pulleys which are connected by the crossed band are running idle.
The poise having arrived at the end of its run and unable to go further, the mitre wheels and the sprocket gearing are stopped, and the two pulleys and the cross belt run idle till the.
A pulley carried on a rotating shaft and connected to another pulley on a second shaft by an endless band consisting of a flat belt, rope, chain or similar connector serves for the transmission of power from the one shaft to the other and is known as a driving pulley; while combinations of pulleys or "sheaves," mounted in fixed or movable frames or "blocks," constitute mechanisms used to facilitate the raising of heavy weights.
Driving pulleys are usually constructed of cast iron, and are of circular form, having a central nave by which they are secured to the shaft by keys or other fastenings, and straight or curved arms connecting the nave to the rim, which latter is of a form adapted to the connector.
Pulleys are usually cast in one piece, and the proportions of the various parts are designed to resist the unknown stresses due to contraction of the casting in cooling, in addition to the stresses to which pulleys are subjected in use.
The combination of these stresses generally limits the rim velocity of cast-iron pulleys to 80 or loo ft.
Benjamin (American Machinist, 1898) on castiron pulleys loaded by a belt to imitate the conditions in practice led him to the conclusion that the rim is usually not sufficiently rigid to load the arms equally, and that the ends of the arms are subjected to bending movements of opposite sign, that at the nave being almost invariably the greater.
Pulleys are also built up of wrought iron and steel, and can then be constructed entirely free from internal stress; they are thus much lighter and stronger, and are not liable to fly to pieces like cast iron if they break.
Pulleys are also made of paper, wood and other materials.
Wooden pulleys are preferably made of maple, the rim being formed of small sections morticed, pinned and glued together, with the grain set in such directions that any warping of the material will leave the cylindrical form practically unaltered.
Wooden pulleys are generally made in two halves, bolted together at the rim and nave, and are provided with wooden spokes dovetailed into the rim and secured by keys.
The rims of pulleys, round which flat bands are wrapped, may be truly cylindrical, in which case the belt will run indifferently at any part of the pulley, or the rim may be swelled towards the centre, when the central line of the band will tend to run in the diametral plane of the pulley.
Parallel shafts may be driven by flexible bands or connectors passing over pulleys, the central planes of which coincide, without any guiding arrangements for the belting.
A common arrangement for driving a lathe spindle, in either direction at several definite speeds, is to provide a countershaft on which are mounted two fixed pulleys and two loose pulleys to accommodate two driving belts from the main shaft, one of which is open and the other crossed.
The belts are moved laterally by the forks of a striking gear pressing on the advancing sides of the belts, and the pulleys are arranged so that the belts either wrap round the loose pulleys, or can be shifted so that one wraps round a fixed pulley, while the other still remains on its loose pulley.
The dimensions of the pulleys are generally so arranged that the return motion of the lathe spindle is faster than the forward motion.
An alternative arrangement consists in providing two loose pulleys on the counter-shaft, driven by open and crossed belts respectively, and arranging two clutches on the shaft, so that by the movement of a sliding block, controlled by hand, one or other of the clutches can be put in gear.
The proportions of cone pulleys for open or crossed belts may be determined by considering the expression for the half length (1) of a belt wrapping round pulleys of radius r 1 and r 2 respectively, and with centres distant c apart.
In determining the dimensions of corresponding drums of cone pulleys it is evident that for a crossed belt the sum of the radii of each pair remains a constant, since the angle a is constant, while for an open belt a is variable and the values of the radii are then obtained by solving the equations r 1 = l/ir - c(a sin a + cos a) + 2c sin a, r 2 = l/7r - c(a sin a +cos_a) - lc sin a.
Repeating this construction for all values of a between o° and 90°, we obtain a curve BPC, which can be used for determining the ratios of corresponding drums of cone pulleys or of conical drums for open belts.
When pulleys are mounted on shafts which are parallel to one another, the band will retain its position, provided that its central line advances towards each pulley in the diametral plane of this latter.
Guide pulleys are set with their diametral planes in the planes containing corresponding pairs of tangents, and a continuous belt wrapped round these pulleys in due order can then be run in either direction.
The rims of pulleys for hemp or other ropes or cords are grooved, and the sides are usually either inclined at 45° or curved to give a sharper angle at the outside than at the bottom of the groove; in the latter case, as the rope wears it engages in a groove of greater angle and less effective grip. Wire ropes are injured by the lateral crushing of the material, and in this case the grooves are wide enough to allow the rope to rest on the rounded bottom, which is lined with leather or wood to diminish the wear and increase the friction.
In English practice there are as many separate endless ropes as there are pairs of grooves in the two pulleys to be connected, but in cases of American practice the rope is continuously wound round the two pulleys, and the free end passes over a pulley mounted on a movable weighted carriage to adjust the tension.