"The Oldham coupling and Schmidt coupling are two various mechanical solutions for transmitting drive between two parallel axles that are not aligned in line".
As wroted on Sariel's Webpage: ( Visit for full explanation, instructions, more information and Moc's)
That makes this two mechanisms an alternative to universal joints, which are long, and to gear wheels, which only fit in specific spacings and affect power/speed ratio if not meshed at 1:1 ratio.
The Oldham coupling consists of two identical rotors, each connected to one axle, and a sliding element between them. In short, the Oldham coupling is short and maintains 1:1 ration, but is complex, fragile and has large diameter.
The Schmidt coupling consists of three discs or triangles connected with links, it can work while its input and output are moving relatively to each other. That makes it an interesting solution for transferring drive to the moving elements of your construction. The Schmidt coupling is also extremely robust and can handle high torque while generating minimum backlash.
A "real" Schmidt coupling, as you can see the Lego Technic version works perfectly...