A rigid coupling is one that does not allow axial or radial motion between the driving and driven shafts. A rigid coupling consists of two flanges, one mounted on each shaft. Rigid couplings require exact alignment between shafts otherwise considerable wear on the bearings and seals will occur.
Rigid couplings are a type of coupling that should only be utilized when shafts are precisely in line. A rigid coupling is only suitable for shafts in close alignment or held in alignment. If not aligned, torque will transfer to the shafts and bearings and likely cause premature failure.