THE EFFICIENCY OF GEARING UNDER FRICTION. 

 Calvin M. Woodward. 



1. The energy lost through the friction of gears, is often 

 ignored, and none of the treatises on Applied Mathematics 

 give a satisfactory treatment of the subject. Moseley's ele- 

 gant discussion is a little involved ; he deals too much with 

 conditions " behind the line of centers;" he fails to give exact 

 results in a finite form ; he furnishes no convenient formulae 

 for showing at a glance the effect of the size of the rolling 

 circle in the case of epicycloidal teeth; and he gives no con- 

 venient material for comparing the efficiency of epicycloidal 

 teeth with the efficiency of involute teeth. 



The following discussion was in substance given to my class 

 nearly two years ago ; I have however recently reduced my 

 equations to such form that the efficiencies of the two kinds 

 of teeth can readily be compared without the trouble of 

 numerical examples. 



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 Figure I, Showing two teeth in action during the "Approach." 



2. General Formulae for all Teeth. Let Fig. 1 represent 

 the geometrical conditions in a plane perpendicular to a pair 

 of parallel axes. C x and 2 are the centers of two wheels, /, 

 their pitch point, r % and r 2 their radii, and T the point of con- 

 tact of two teeth. TI is the common normal to the teeth in 



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