893 



WHEEL. 



WHEEL. 



994 





and endless lands 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 band-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 carrying-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 tettJi, '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. Co^r-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. Trmidle- 

 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 ; <T<HCT!-wheels are those in which the teeth are cut out of the 

 rim of the wheel ; antor-wheels are those in which the teeth are cut 

 upon the inner surface of the rim ; ' rjli, '/-wheels are those in which 



the faces of the teeth are portions of cones whose apices meet, anil are 

 inclined so as to allow the motion of the first, or e/riri</-wheel to be 

 changed in its direction ; />Kr-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 thejirst motion 

 ir ilri'-'niii wheel; the secondary wheel is called the folloicer, or the 



in the case of cog-wheels, but sometimes it is called the ?" 

 in the ca.sc 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 p/ate-wheels ; the inner rim of a 

 first motion annular-wheel is known by the name of the annului. 

 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 cm. 

 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. 



In setting out a wheel, the basis of the operation is the piteh circle, 

 or the working circumference ; the term pitch itself means the distance 

 apart of the centres of tho teeth upon that circle. The only condition 

 which regulates the pitch is, that the material should be strong enough 

 to bear the effort to which it is to be exposed ; and in practice it is found 

 that cast-iron wheels work satisfactorily with pitches varying between 1 

 and 3 inches in large wheels, and between a quarter of an inch and three 

 quarters of an inch in very small ones. The number of teeth depends 

 upon the circumference, and upon the pitch ; or calling the number of 



teeth n, the circumference c, and the pitch ;<; then n , all the 



dimensions being in inches ; or the diameter d will be found by making 

 p n 



~ 



j~JY^ The velocities at which the various wheels of a piece of 



machinery are required to revolve determines their respective diameters, 

 and they are calculated upon the principles to be described in the 

 sequel ; but it is to be observed that the true, radii are always rather 

 larger than the primitire radii, which latter serve to define the pitch 

 circle; the true radii, on the contrary, define the extremities of the 

 teeth. Another general law is that the number of teeth in the xpur- 

 (or driving-) wheel is to the number of teeth in the pinion (or follower) 

 in the ratio of their respective radii ; or calling the diameter of the 

 pur-wheel A B ; the diameter of the pinion c D ; and the number of 

 teeth on the former n ; then the number of teeth on the pinion will be 

 found thus : A B : c D : : H : . The outlines of the teeth are ascer- 



tained by dividing the pitch circle into equal parts corresponding with 

 the proposed number of teeth ; the pitch is then subdivided into foiu- 

 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 piniou are formed by portions of 

 a hypocycloid 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 side 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 v,th or s ' th 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 annulus must be 

 portions of a hypocycloid. The portion of the tooth beyond the pitch 

 circle, to which the above peculiar forms are given, is occasionally 

 known by the name of the addendum, and it is usually about ^ths 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 : 



Depth of addendum . , 

 Working depth, from addendum to flank 



Whole depth 



Thickness of tooth on pitch lino . 

 Breadth of space on ditto . . 



of pitch. 



T'T 



A 



In small wheels with few teeth the depth of the addendum must be 

 increased above the proportion above-mentioned. 



Berilled gearing consists of frustra of cones, which are supposed to 

 roll upon one another, and whose apices are supposed to meet in one 

 point ; and in this case the form of the addenda ought to be a portion 

 of a spherical epicycloid, according to strict theory, but in practice a 

 much more simple form, devised by Telford, and described in Buchanan's 

 ' Treatise on Mill-work,' p. 58 (1841), is used. Indeed, it is very rarely 

 that the faces of wheels are made with cycloidal forms of any descrip- 

 tion ; and practical men adopt, instead of them, simpler circular forms. 

 Professor Willis^ in his 'Principles of Mechanism,' tins described an 

 instrument of his own invention, for drawing the teeth of wheels by 

 arcs of circles ; and has accompanied the description by tables illus- 

 trating its use. The reader is referred to the various books above 



specific details with respect to the principles upon which teethed wheels 

 of the various kinds enumerated are designed. Professor Willis's 

 ' Principles of Mechanism ' may, perhaps, be cited as containing tho 

 most valuable information on the subject. 



It is necessary here to add that in some cases it is desirable to pro- 

 duce in machinery an intermittence in its action, or a certain alterna- 

 tion of motion and of rest, in the wheels gearing into one another. 

 Tlii.s is effected by leaving a portion of the circumference of the 

 driving-wheel without teeth for a length corresponding with the 

 desired period of repose ; precautions, however, must be taken to 

 insure that the teeth should fall into their proper places when contact 

 is restored, for which purpose pins and guides on the face of the 

 wheel are commonly introduced. Xatchet-vfheels, or those which only 

 revolve in one direction, and have a species of alternate reciprocating 

 action on the driver (in this sense, that they are raised gradually for a 

 certain portion of the revolution, and are then suddenly released), are 

 introduced for the purposes either of preventing the wheel-work from 

 revolving in more than in the direction originally selected, or for ob- 

 taining alternate vertical or horizontal motion in the shafts of a piece 

 of machinery. The pin which prevents the alteration of the rotation 

 of a ratchet-wheel, is usually placed on a pivot, and is able to be thrown 

 out of gear at will: it is commonly known by the name of a pnnll. 

 Mill work of all kinds may either be kept permanently in gear, or it 

 may be constructed so as to allow any of its parts to work, or to rest, 

 independently of the general combination, by means of couplings, 

 clutch-boxes, friction, or reversing-gear. In the construction of ma- 

 chinery, wheels play very important parts by the action of drivers 

 upon the various combinations for producing change of motion, such 

 as racks, endless screws, cams, eccentrics, teethed arcs, &c. ; but the 

 consideration of these functions of wheels, as also of those by which 

 they are made to regulate the motion of the machinery to which they 

 are attached, by reason of their power of retaining momentum, belongs 



