Machine Design
Oldham coupling is used to connect two shafts

Which are not in exact alignment
Which have lateral misalignment
Which are perfectly aligned
Whose axes intersect at a small angle

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Machine Design
A fast and loose pulley drive is used when

Shafts are arranged parallel and rotate in the same directions
Shafts are arranged parallel and rotate in the opposite directions
Driven shaft is to be started or stopped whenever desired without interfering with the driving shaft
Shafts are arranged at right angles and rotate in one definite direction

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