LAW OF GEARING

Law of Gearing  :-

Consider the portions of two gear teeth in mesh.

O1 and O2 are centre points.

Let K= point of contact T T = Common tangent at point of contact K

N’N’ = Common Normal at point of contact K 

O1M and O2N are perpendicular to Common Normal N’N’.

V1 and V2 =Velocities at point K w. r. t. gear 1 and 2 respectively If mating teeth to remain in contact while transmitting motion, components of velocities must be equal along N’N’. So, V1cos  = V2 COS   (ω1 x O1K) cos  = (ω2 x O2K) cos   From triangles O1MK and O2NK putting values of cos   and COS    ω1 X O1K X        =ω2 X O2K X     

 ω1 X O1M =ω2 X O2N       =               …………..(1) Since  O1MP and O2NP are similar triangles.

     

=     

          …………..(2)

From equations (1) and(2) , we get

    =     

 From this, it is proved that angular velocity ratio is inversely proportional to ratio of distance of fixed point ‘P’ ,which is pitch point. This gives constant angular velocity ratio.

In other words, the common normal at the point of contact between a pair of teeth must always pass through the pitch point for all positions of mating gears. This is the fundamental condition which must be satisfied while designing the profiles of teeth for gears.

This is Law of Gearing or Condition of correct gearing.