Theory of Machine
The instantaneous center of a rigid thin disc rolling on a plane rigid surface is located at

An infinite distance on the plane surface
The center of the disc
The point of contact
The point on the circumference situated vertically opposite to the contact point

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Theory of Machine
The contact ratio is given by

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

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