Theory of Machine
Oldham's coupling is the

Second inversion of double slider crank chain
Second inversion of single slider crank chain
Third inversion of double slider crank chain
Third inversion of slider crank chain

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Theory of Machine
The relation l = (2/3).(j + 2) apply only to kinematic chains in which lower pairs are used. This may be used to kinematic chains in which higher pairs are used, but each higher pair may be taken as equivalent to

One lower pair and two additional links
Any one of these
Two lower pairs and two additional links
Two lower pairs and one additional link

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