96 Trans. Acad. Sci. of St. Louis. 



action, and the angle the normal makes with the line of 

 centers. The arrows show the directions of rotations, C 1 

 being the driver. 



While the friction is not a function of the velocity, it is 

 convenient to employ their angular velocities a x and a 2 . 

 During the" approach " to the pitch point the two teeth are 

 sliding towards each other, the velocity of sliding being 

 measured by the familiar expression r (a x + a 2 ) 9 r being the 

 distance of the point of contact from the pitch point. Let- 

 ting the co-efficient of friction be/, it is evident that the line 

 of resultant action between the teeth makes an angle <p with 

 the normal such that tan <p = f. The action of the driving 

 tooth is then along the line P } TJP 2 . The magnitude of that 

 action we will call P ; so that the driving moment is P^ = M l ; 

 and the moment transmitted to the follower is M 2 = Pl 7 . 

 From the notation shown in Fig. 1, it is easily seen that 



^V, sin (0 — <p) +rsin^ > ^ 



Z 2 = r 2 sin(0 — <p) — rs'm<p 5 



a 





\ 



Figure 2, Showing two teeth in action during the *' Recess." 



After the point of contact has passed the pitch point, and 

 the teeth are separating, the line of resultant action is on the 

 other side of the normal, as is shown in Fig. 2. In this case 



i; = r 2 sin {6 + <f) + r sin <p 1(2) 



l 2 = r 2 sin (6 + (p) — r sin <p $ 



