Theory of Machine
The velocity of sliding of meshing gear teeth is (Where ω₁ and ω₂ are angular velocities of meshing gears and ‘y’ is distance between point of contact and the pitch point)
The velocity of the instantaneous centre relative to any third rigid link is same whether the instantaneous centre is regarded as a point on the first rigid link or on the second rigid link.
The two rigid links have no linear velocity relative to each other at the instantaneous centre.
A rigid link rotates instantaneously relative to another link at the instantaneous centre for the configuration of the mechanism considered.