Theory of Machine
The contact ratio is given by

(Length of the path of approach)/(Circular pitch)
(Length of the arc of approach)/cosφ
(Length of the arc of contact)/(Circular pitch)
(Length of path of recess)/(Circular pitch)

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Theory of Machine
The inversion of a mechanism is

Changing of a higher pair to a lower pair
Obtained by fixing different links in a kinematic chain
Obtained by reversing the input and output motion
Turning its upside down

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