Theory of Machine
Whitworth quick return mechanism is obtained by inversion of

Slider crank mechanism
Roller cam mechanism
Kinematic chain
Five link mechanism

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Theory of Machine
The contact ratio is given by

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

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Theory of Machine
In elliptical trammels

All four pairs are turning
Two pairs turning and two pairs sliding
Three pairs turning and one pair sliding
One pair turning and three pairs sliding

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