The friction wheels of mill-work ere introduced for the same purpose that wheal, are adapted to ordinary carriages ; that is to say, for the purpose of converting sliding friction into rolling friction. They are used to facilitate the horizontal or vertical movement of traversing beds, of guide rods, fie., and therefore the only conditions they are 'required to fulfil are, that they should revolve freely on their own axles, and present smooth surfaces (able to retain a lubricating fluid) to the bodies moving over them, or over which they may move. Driving band-wheels, on the contrary, are fixed on their bearing shafts, and have their surfaces formed in such a manner as to cause the straps, or bands, to adhere to them by their mere friction upon the asperities, and thus to produce motion in the secondary band-wheels of the machinery to which they aro applied, by the rotation of the first wheels. In some cases also, motion Is communicated by means of wheels whose surfaces are in contact, and which act upon one another by the mere unevenness of those surfaces ; if, however, any serious resistance should be encountered, the wheels would be likely to elide over one another, and they are therefore only used in light and delicate machinery. Indeed all descriptions of band-wheels are exposed to the same objection, because they only communicate motion by the friction of the bands upon the respective surfaces, and when the resistance exceeds that friction, the bands must slide over the wheels ; but they present so many facilities for the introduction of speed pulleys, (that is to say, of pulleys by means of which the rate of revolution may be modified at will) that they are constantly resorted to in machinery, especially when it is desirable to avoid making a noise. Band-wheels are commonly arranged so as to present on the Name axle, and in immediate proximity to one another, what are called fast and loose pulleys ; the fast pulleys: being fixed upon the axle, so that the two must turn together, whilst the loose pulley turns freely upon the axle, and does not communicate any motion to the latter. When, therefore, it is desired to put band-wheels with fast and loose pulleys out of gear, all that is required to be done is to pass the band upon the loose pulley, and the communication of the movement immediately ceases.
Band-wheels also present great advantages from the ease with which they admit of the change in the direction of the motion. If, for instance, it be desired to reverse the motion, the baud is simply crossed, and endless bands may be made to communicate motion in every possible direction with respect to the driving pulley. Long bands are, however, objectionable, as they have a tendency to stretch ; and it must also be observed that the circumferences of bend-wheels should be made slightly rounded, because there is a tendency in bands running over pulleys to work towards the portions of those pulleys which are of the largest diameter ; and thus, perhaps, to "cast off." The friction cones, used by rope-spinners, may be cited as amongst the most valu able illustrations of the use of these modifications of wheel-work ; as may also be cited the speed pulleys of lathes, the earqing-bands of printing machinery, the friction-rollers upon which the endless sieves of paper-making machines traverse, &c.
In teethed wheels, a series of projections, or teeth, 'are formed on the outer rim of one wheel, which work into corresponding projections upon the outer rim of the wheel connected with it, in such a manner as to allow the teeth of the former to communicate their motion by the sliding or rubbing of their surfaces upon the surfaces of the teeth of the second wheel. Cog-wheels are those in which the teeth are made of a different material to the wheel itself, but the cogs are never theless of the same outline in principle as ordinary teeth. Trundle wheels are those in which the teeth are formed by cylinders of small diameter, and short lengths, fixed between two discs ; they are much used in coarse mill-work, on account of the smoothness of their action, and the small friction to which they give rise. Pin-wheels are those
in which similar cylinders are placed upon the surface of a revolving disc ; croren-wheels are those in which the teeth are cut out of the rim of the wheel ; annular-wheels are those in which the teeth are cut upon the inner surface of the rim ; berilted-wheels are those in which tamed by dividing the pitch circle into equal parts corresponding with the proposed number of teeth; the pitch is then subdivided into four parts, to obtain the centres of the intervals, and also the flanks of the teeth within the line of the pitch circle. Beyond that line the flanks of the spur teeth are formed by portions of-an epicycloid generated by the revolution of a circle, whose diameter is equal to the radius of the pinion pitch circle around the pitch circle of the spur ; and the flanks of the extremity of the teeth of the pinion are formed by portions of a hypocyeloid generated by the revolution of the circle before named on the interior of the pitch circle of the pinion itself. The projection of the teeth beyond their respective pitch circles is regulated by the condition that the epicycloidal and hypocycloidal curves shall be suffi ciently long to cause the Latter to bear upon the aide of the teeth, through an extent of circumferential movement equal to the length of the pitch. Practically this length may be found by describing a circle of a diameter equal to the radius of the pinion upon the line of centres, and at the point where it intersects the radial line forming the flank of the second tooth, describing the true radius of the spur. The depth of the intervals is made so as to leave a small space between the extremity of the teeth and the rim, and it is customary to leave a little play between the teeth, equal to about ;,th or .5th of the pitch ; the interior angles of the teeth are rounded off in order to increase their strength. In setting out a pinion intended to drive a lantern-wheel, the teeth must still be made portions of epicycloids ; but in the case of racks driven by teethed pinions the curves must be involutes of the pitch circle, and in annular wheels the teeth of the annulue must be portions of a hypocycloid. The portion of the tooth beyond the pitch circle, to which the above peculiar forma are given, is occasionally known by the name of the addendum, and it is usually about the of the pitch employed. In common construction the proportions of the various parts of a pair of teethed wheels gearing into one another are as follows :— the faces of the teeth are portions of cones whose apices meet, and are inclined so as to allow the motion of the first, or driring-wheel to be changed in its direction ; spur-wheels are those which transmit motion in directions parallel to that of the revolution of the driving-wheel. The first wheel in all these instances bears the name of the first motion or driring-wheel ; the secondary wheel is called the follower, or the pinion in the ewe of cog-wheels, but sometimes it ie called the wallower, in the case of trundle-wheels. The wheels themselves are composed of the central boss, the arms, and the rim, bearing the teeth ; sometimes, however, in small pinions the arms are replaced by a solid plate, and then they are known by the name of plate-wheels; the inner rim of a first motion annular-wheel is known by the name of the annulus. When it is essential that no sliding should take place on the surfaces of wheels the faces are broken into what are called compound or combined wheels, which consist of a series of parallel concentric ranges of teeth, so placed that the contact of any pair of teeth should only be momentary. Dr. Hooke introduced this kind of wheel, and indeed it is at times known by his name ; but it is too complicated, and too liable to fracture, for ordinary work.