Coupling are used for transmitting torque between two shafts even when they are misaligned. For hobbyist CNCs they are used to connect the Stepper Motor axis and the leadscrew/ballscrew.
The basic (and worst) coupling is the rigid couplings:
This coupling is good for transmitting torque between two shafts and has no backlash but doesn’t allow misalignment among shafts and will wear or damage the shafts very soon.
The Oldham coupling has 3 discs (normally two metal discs and one plastic disc) and allow parallel shaft misalignment (offset) :
Oldham coupling can reduce the backlash, but there are better options as we will see next.
As known as Spider Coupling or Lovejoy Coupling:
The Jaw coupling has 2 metal discs and an elastomer filling disc internally. They are good for torque transfer and damping support, but have some backlash.
As known as Beam coupling is a hollow cylinder with helical cut:
This coupling can support some degrees of misalignment and have low backlash.
Bellows coupling is a type of cylinder cut or electro-deposited to become a bellow:
This type of coupling allow misalignment and the lowest backlash of “flexibles couplings”.