A self-aligning mud pump apparatus is provided. In one embodiment, the mud pump includes a rotatable crankshaft, a crosshead, a crosshead guide, and a hub disposed in a housing. The hub is disposed on the crankshaft and is operable to convert rotating motion of the crankshaft to reciprocating motion of the crosshead within the crosshead guide. The hub is coupled to the crosshead via a connecting rod, which is connected the crosshead such that the connecting rod has five degrees of freedom with respect to the crosshead guide. The mud pump may also or instead include a piston coupled to the crosshead with five degrees of freedom between the piston and the crosshead. Additional systems, devices, and methods are also disclosed.