THE LEVER AND WHEELWORK. 



263 



it, spur gear is generally used. Thus, in fig. 27, the three axes are parallel 

 to each other. If a motion round one axis is to be communicated to another 

 at right angles to it, a crown wheel, working in a spur pinion, as in fig. 29, 

 will serve ; or the same object may be obtained by two bevelled wheels, as in 

 fig. 30. 



If a motion round one axis is required to be communicated to another in- 

 clined to it at any proposed angle, two bevelled wheels can always be used. 

 In fig. 31, let A B and A C be the two axles ; two bevelled wheels, such as 



Pig. 31. 



D E and E F, on these axles will transmit the motion or rotation from one to 

 the other, and the relative velocity may, as usual, be regulated by the propor- 

 tional magnitude of the wheels. 



In order to equalize the wear of the teeth of a wheel and pinion, which work { 

 in one another, it is necessary that every leaf of the pinion should work in 

 succession through every tooth of the wheel, and not continually act upon the 

 same set of teeth. If the teeth could be accurately shaped according to math- 

 ematical principles, and the materials of which they are formed be perfectly | 

 uniform, this precaution would be less necessary ; but, as slight inequalities, < 

 both of material and form, must necessarily exist, the effects of these should be > 

 as far as possible equalized, by distributing them through every part of the 

 wheel. For this purpose, it is usual, especially in millwork, where considera- 

 ble force is used, so to regulate the proportion of the number of teeth in the 

 wheel and pinion, that the same leaf of the pinion shall not be engaged twice 

 with any one tooth of the wheel until after the action of a number of teeth, ex- 

 pressed by the product of the number of teeth in the wheel and pinion. Let 

 us suppose that the pinion contains ten leaves, which we shall denominate by 

 the numbers 1, 2, 3, &c., and that the wheel contains 60 teeth similarly de- 

 nominated. At the commencement of the motion, suppose the leaf 1 of the 

 pinion engages the tooth 1 of the wheel ; then, after one revolution, the leaf 1 

 of the pinion will engage the tooth 1 1 of the wheel, and after two revolutions 

 the leaf 1 of the pinion will engage the tooth 21 of the wheel, and in like man- 

 ner, after three, four, and five revolutions of the pinion, the leaf 1 will engage 

 successively the teeth 31, 41, and 51 of the wheel. After the sixth revolution, 

 the leaf 1 of the pinion will engage the tooth 1 of the wheel. Thus it is evi- 

 dent that, in the case here supposed, the leaf 1 of the pinion will continually 

 be engaged with the teeth 1, 11, 21, 31, 41, and 51 of the wheel, and no oth- 

 ers. The like may be said of every leaf of the pinion. Thus the leaf 2 of the 

 pinion will be successively engaged with the teeth 2, 12, 22, 32, 42, and 52 

 of the wheel, and no others. Any accidental inequalities of these teeth will 

 therefore continually act upon each other, until the circumference of the wheel 

 be divided into parts often teeth each, unequally worn. This effect would be 

 avoided by giving either the wheel or pinion one tooth more or one tooth Jess. 

 Thus, suppose the wheel, instead of having 60 teeth, had 61, then, after six 

 revolutions of the pinion, the leaf 1 of the pinion would be engaged with the 



