NOTE ON FRICTION WHEELS. 



It was observed, that a rolling continuous curve cannot drive another after 

 the driving point has reached its maximum distance : if, however, the curves are 

 discontinuous, and a new driving point shall come into action at the moment the 

 former driving point shall have reached its maximum distance, a continued revolv- 

 ing motion without friction, may, under certain circumstances be produced ; and 

 this will be the case if two wheels be formed of semilobes of the same system, if 

 clogging of the wheels can be avoided ; for (fig. 23) when the driving point of 

 A has arrived at G, a new driving point will come into action at B. 



The variation of the angular velocity of the wheel driven, supposing that of 

 the driving wheel to be uniform ; the oblique mechanical action of the driving 

 wheel near the apses, which at the apses is towards the centre, and the shocks pro- 

 duced at the change of the driving points, which would however be received at the 

 flat surfaces, would unfit such wheels for the purpose of moving weights ; it may 

 still be a question, whether they might not be successfully employed for purposes of 

 motion. 



When the new driving point comes into action, it is necessary that the point 

 F should clear itself of the point G. The relative motions of the wheels will be 

 the same if the wheel B be supposed at rest, and the other to move round it ; 

 and therefore the point F must describe a curve without the wheel B, or the 

 radius of curvature of the curve described by the point F, immediately after the 

 change of the driving points, must be less than the radius of curvature at G, sup- 

 posing the curvature at G to be convex towards the centre of B; in which case, 

 the wheels will not clog at G, when the driving point is changed. 



Let R be the radius of curvature described by F; if the wheel A be sup- 

 posed to have moved a little, the motion of F will be perpendicular to FC ; and 

 GH, FH being consecutive normals, FH will be the radius of curvature of the 

 curve described by F, CD the radius of curvature of the wheel B at the major 

 apse, and CE that of A at the minor apse. 



12 



