942

THEORY AND PRACTICE OF ENGINEERING.

Book 11.

When a wheel and pinion actwith each other, the teeth of thesmall wheel may be made torepresent the staves of a trundle;suppose the teeth divided on thepitch lines EE, FF: on thewheel C form circles, which mayrepresent staves; the centre ofone of these staves or teeth beingplaced on the line of centres at A,draw' the line A B, uniting thecentres of these teeth.

Then the radius A b from A asa centre will describe be, thecurve of the tooth of the conducting wheel, and the curve ba that of the other wheel.Radius being equal to pitch, diminished by half the diameter of the circle of the stave teeth,and as the centres will alw'ays be in the pitch lines, the other teeth may be easily drawn.

Bevelled Gear , or conical wdieels, are usually frustra of fluted cones; the axis or shaftof the leader or driver is placed at an angle of 45 degrees with the axis of the shaftof the follower or driver. To form a pair of conical wheels there must be set out on thefrustra regular series of teeth at equal distances, projecting as much above the surface asthe hollow between them descends, 'lliese teeth must be directed towards the apex, sothat when they are in contact, they shall touch each other along the whole length ; w’henthe point of contact is along the line of centres, there is little or no friction. Wheels ofthis kind are used to communicate motion in any direction that is required, and the actionof the teeth is the same as in the common spur-wheels; the diminution of the teeth being inthe same ratio in both cases, but requiring more attention in the setting out than the common

Fig. 1289. Fig. 1290.

teeth.

Supposing it is required to determine the diameter of two wheels that shall change amotion into a direction of the angle above mentioned, and in which the axle shall movewith four times the velocity; the wheel mounted on the axis that is to revolve four timesmore rapidly, must have one-fourth the number of teeth, and one-fourth the diameter.

Let the cone A C D have its slant height atright angles to C B 1); the cone will then inter-sect the teeth at right angles.

If AB show the original direction of themotion to be changed, through the point Odraw CO D at an angle of 45 degrees to the lineA B. The axle CD is required to move fourtimes more rapidly than AB; the wheel whichit carries must have only one-fourth the numberof teeth. Draw cd at any distance parallel toCD. and ab parallel to AB, so that Aa=B6= 4 Cc = 4 Dr/, and join the points of intersectioni in O : draw’ Om, so that the angle B O w equalsBO<, and 0«, so that DOn equals DOi, andthese lines show the size and position of the conesof which the wheels are to be formed. Theangle BOD is in fact divided into two angles,wdiose sines are to one another as the number ofrevolutions of one wheel is to the number of re-volutions of the other.

The surface of the cone may be developed ona plane by rolling it round its apex, and by thismeans the true impression of its teeth taken ; thepitch circumference of C D will be the sector ofa circle, the slant height B C being radius.

The wheel and pinion may be either situatedon the same plane, or their planes may form anangle, in which case one of them becomes thecrown wheel, or both of them may be bevelled,and their teeth cut obliquely : according to therelative magnitude of the wheels, the angle of thebevel must be different, in order that theirvelocities may be in the same proportion at bothends of their oblique faces ; for which purpose, it

Fig. 1291.

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Fig.1292.

becomes necessary that the teeth must be directed to the point where the axes would meet.Some mechanics have considered that the angles should be as the diameters of the wheel,