Theory of Machine
The example of spherical pair is

Ball and socket joint
Bolt and nut
Ball bearing and roller bearing
Lead screw of a lathe

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Theory of Machine
The contact ratio is given by

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

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