MECHANICS. 



The teeth should, therefore, be so 

 formed as to remove these defects ; for 

 which purpose it would be necessary 

 that they should act in such a manner, 

 that, 



1st. The teeth of one wheel should 

 press in a direction perpendicular to the 

 radius of the other wheel ; or, in other 

 words, the pressure should be tangential 

 to the wheel which is driven. 



2d. As many teeth as possible should 

 be in contact at the same time, in order 

 to distribute the pressure amongst them, 

 and thereby to diminish the pressure 

 upon each tooth. This arrangement will 

 diminish the wear, and the chances of 

 fracture. 



3rd. During the entire action of one 

 tooth upon another, the direction of the 

 pressure should be the same, in order 

 that, acting with the same leverage, the 

 effect may be uniform. 



4th. The surfaces of the teeth in work- 

 ing should not rub one upon another, 

 and should suffer no jolt either at the 

 commencement or termination of their 

 mutual contact. 



Various forms have been suggested 

 for the teeth, with a view to the accom- 

 plishment of some or all of these advan- 

 tages : but that which seems best calcu- 

 lated to attain the desired ends is the 

 following : 



Suppose that F H I, fig. 45, is the cir- 

 cumference of the wheel on which it is 

 proposed to raise teeth, and let H 



Fig. 45. 



be one of the points from which the side 

 of a tooth is to spring. Suppose a 

 string is attached to the circumference 

 of the wheel as at I, and applied to the 

 circumference I F, an.l terminated at 



H carrying a pencil at its extremity. 

 Let the string, being constantly stretched 

 tight, be rolled off, so that that part of 

 it, F C, which has been at any time dis- 

 engaged from the circumference of the 

 wheel shall be in a straight line, touch- 

 ing the circumference at F, and in this 

 way let the pencil describe the curve* 

 H Cg. Let a H be the breadth of the 

 tooth at the circumference of the wheel ; 

 and attaching a string in like manner to 

 the other side of the wheel, and rolling 

 it on in the opposite direction, so that 

 its extremity bearing the pencil shall be 

 at a, let a similar curve be described. 

 These two curves will include a space 

 which will represent the form of a tooth 

 which will accomplish all the purposes 

 and possess all the advantages we have 

 mentioned. 



The teeth of the pinion, of course, are 

 to be formed in the same manner. 



It is a remarkable property of these 

 curves that a line F which touches 

 both circles will pass through the point 

 of contact of the teeth, and not only of 

 one pair of teeth, but of every pair 

 which are in contact : and this line will 

 be perpendicular to the direction of the 

 surfaces of the teeth at the point of 

 their mutual contact. Thus the pres- 

 sure of the pinion on the wheel is ex- 

 erted tangentially to both, and therefore 

 acts always with the same leverage and 

 to the greatest advantage. 



Further, during the whole period of 

 the contact of any two teeth, the pressure 

 acts in the same' direction and with the 

 same force, and therefore when it is 

 uniform, it necessarily produces an 

 uniform effect. 



During the motion, the surface of one 

 tooth does not rub or scrape against the 

 surface of the other, but the one rolls 

 upon the other, thereby removing 

 nearly all the effects of friction, nid 

 diminishing considerably the wear of 

 the machinery, and the waste of the 

 power. 



Several teeth are in contact at the 

 same time, and all working with equal 

 power, so that the stress is 'equally dis- 

 tributed among them, and the chances 

 of fracture are greatly diminished. 



Thus this form of "tooth has all the 

 advantages which can be desired. 



(68.) In regulating the number of 

 teeth in the wheel and the pinion which 

 works it, it should be so contrived that 

 the same teeth should be engaged as 



This curve U called the involute of the circle. 



