The invention relates to an axial piston machine of a kind that has a plurality of pistons each reciprocating in a respective cylinder in a direction substantially parallel or at an angle less than 30 degrees to a crankshaft axis. The crankshaft axis presents a crank that is at an angle to the crankshaft axis and to which a reciprocator is mounted. The reciprocator effects the controlled movement of the pistons in their cylinders via a connection mechanism that connects each said piston with said reciprocator. The machine includes at least one pair of rotational constraint mechanisms to constrain the movement between the reciprocator and the pistons.