The Ratchet-wheel and Detent. Fig. 17. 27. In fig. 17, A represents the ratchet-wheel and D the detent, falling into the angular teeth of the ratchet, thereby admitting the wheel to revolve in the direction of the arrow, but at the same time preventing it from revolving in the opposite direction. In certain kinds of machinery, the action of the moving force undergoes periodic intermissions; in such cases the ratchet and detent are used to prevent the recoil of the wheels, and D sometimes to give an intermittent motion to the wheel, as in the following example. Intermittent Motion produced by Link-work connected with a Ratchet-wheel. D Fig. 18. 28. BE is a rod, turning on the fixed centre B, to which a reciprocating motion is given by the connecting rod c of a crank, or by any other means; E F is a click, jointed to the rod в E at its extremity, and gives motion to the ratchet-wheel A. At each upward stroke of the rod B E, the click E F, acting upon the saw-like teeth of the ratchet-wheel, causes it to move round one or more teeth; and when the extremity F of the click is drawn back by the descent of the lever B E, it will slide over the bevelled sides of the teeth without giving any motion to the wheel, so that at every upward stroke of the rod c the ratchet-wheel will be moved round, and it will remain at rest during every downward stroke of the rod. Thus the reciprocating motion of the connecting rod c will produce an intermittent circular motion in the axis A. B III. ON WRAPPING CONNECTORS. 29. When the moving force of the machinery is not very great, cords, belts, and other wrapping connectors are most usually employed in transmitting motion from one revolving axis to another. 30. The endless cord or belt A B C D, represented in figs. 19 Fig. 19. D B K C R Fig. 20. D B K and 20, passes round the wheels A B and C D, revolving on the parallel axes R K and Q F, and transmits motion from the axis QF to the axis R K, with a constant velocity ratio. In all such cases the motion is entirely maintained by the frictional adhesion of the cord or belt to the surface of the wheel. When the cord passing round the wheels is direct, as in fig. 19, the motions of the wheels take place in the same direction, and when the cords cross each other, as in fig. 20, the motions of the wheels take place in opposite directions. If the wheel C D makes one revolution, then Or putting R and r for the radii of the wheels C D and A B respectively, and Q and q for their respective synchronal rotations, then Example.-If the radius of the wheel C D be 12 inches, and that of A B 9 inches, what will be the least number of entire revolutions which they must make in the same time? The fraction 12 9 reduced to its least terms is 4, therefore the least number of synchronal rotations are 4 and 3; that is to say, whilst the wheel C D makes three rotations, the wheel A B will make 4. 31. Fig. 21 represents a system of three revolving axes, in which motion is transmitted from one to the other, by means of a series of belts. The belt being direct in the wheels A and D C, their axes will Fig. 21. Н D I A C G move in the same direction, but, as the belt crosses in passing from D C to H G, their axes will move in opposite directions. Here, whilst the axis в makes one rotation, the Or putting R1 =rad. D C, R2=rad. H G, &c., r1=rad. I K, r2=rad. E F, &c., and putting q and Q for the synchronal rotations of the first and last axes respectively; then Example.-In the mechanism represented in fig. 21, let R1 = 8, R2=15, r1=5, 7, 4; required the least number of entire rotations performed in the same time by the axes a and B. Here, by eq. (2) we have that is, whilst the axis в makes one revolution, the axis A will make six. 32. In raising buckets from deep wells or from pits, a continuous cord coils round an axle or a drum wheel, as the case may be, the full bucket being attached to one end of the cord and the empty bucket to the other end; the rotation of the axle coils up the cord to which the full bucket is attached and at the same time uncoils the cord to which the empty one is attached, so that whilst the former is ascending the latter is descending. Fig. 22. B Speed Pulleys. 33. Fig. 22 represents an arrangement of speed pulleys; A B and C D are two parallel axes, upon each of which is fixed a series of pulleys, or wheels, adapted for a belt of given length, so that it may be shifted from one pair of wheels to any other pair, say, for example, from the pair a a1 to the pair c c1 In order to suit this arrangement, if the belt be crossed, the sum of the diameters of any pair of pulleys must be a constant quantity, that is to say, it must be equal to the sum of the diameters of any other pair. By this contrivance, a change in the velocity ratio of the two axes is produced by simply shifting the belt from one pair to another. In practice it is customary to make the two groups of pulleys exactly alike, the smallest pulley of one being placed opposite to the largest of the other. = In a group of speed pulleys, let s the constant sum of the diameters of the driver and follower, D=the diameter of the driver, d=the diameter of the follower, and Q, q the number of their synchronal rotations respectively; then Q d and D Example.- Required the diameters of a pair of speed pulleys, when the sum of the diameters is 30 inches, and the driver makes two revolutions, whilst the follower makes 3. Here s=30, Q=2, and q=3; then by eq. (1) and (2) we have If the constant sum of the diameters of a group of 5 pairs of speed pulleys be 12 inches, and the diameters of the pulleys a1, b1, c1, d1, e1, be 10, 8, 6, 4, and 2 inches respectively, then the diameters of the pulleys a, b, c, d, e, will be 2, 4, 6, 8, and 10 inches respectively; and as the strap is shifted from one pair of wheels to another, the relative velocities of the axes CD and AB will be as the numbers,, 1, 2, and 5. 34. It is customary to construct the pairs of speed pulleys so that the rotations of the follower may be increased or decreased in a certain geometric ratio. Thus, if r be this ratio, then for 5 pairs of speed pulleys we shall have the series of terms Պ 1 1 1, r, r2, for the different values of 2, the ratio of the synchronal q rotations of each pair. Or generally if ʼn be the number of pairs, In this case, let D1, D2, D" the diameters of the 1st, 2nd, and nth pulleys, respectively, on the driving axis; and these symbols, taken in a reverse order, will be the corresponding diameters of the pulleys on the driven axis; then of the different pairs) shall have the common ratio of 3, the constant sum of the diameters of each pair being 26 inches. 5, and S = 26, then from the foregoing Here r = formulæ we find n = But the remaining diameters will be better found as follows: D= 26 - 18 = 8; D4 = 26 |