Couplings are generally classified as rigid coupling and flexible coupling.

When both driving and driven shafts are coaxial to each others.

Flexible coupling can absorb misalignment between driving and driven shafts while rigid coupling cannot.

Parallel misalignment - Offset distance between centerlines of driving and driven shafts

Angular misalignment - Angle between centerlines of driving and driven shafts

Axial displacement - movement of shafts in axial direct due to thermal growth, floating rotor, etc.

Different types of flexible couplings suitable for different applications, such as large parallel misalignment, large angular misalignment, low torque high speed situation, low torsional stiffness, large torque fluctuations, etc