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

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Theory of Machine
The magnitude of velocities of the points on a rigid link is

Directly proportional to the distance from the points to the instantaneous center and is perpendicular to the line joining the point to the instantaneous center
Inversely proportional to the distance from the points to the instantaneous center and is perpendicular to the line joining the point to the instantaneous center
Inversely proportional to the distance from the points to the instantaneous center and is parallel to the line joining the point to the instantaneous center
Directly proportional to the distance from the points to the instantaneous center and is parallel to the line joining the point to the instantaneous center

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