Abstract: An axial cylinder machine includes a shaft, journaled in one end of a housing to turn about its axis and a plurality of cylinders. A spider is mounted inside the housing by means of a main swivel connection to swivel about a center which is disposed along the shaft axis and the spider includes a plurality of arms, one for each cylinder, projecting generally radially from the center with one projecting in under each cylinder. Each cylinder includes a rod, one end of which swivels on the piston sliding in the cylinder and the other end of which is connected by a swivel connection to the outer end of the associated arm of the spider. As a result, the spider swivels with a generally circular motion about its center when the pistons are successively reciprocated or vice versa. The main swivel connection comprises a stationary shallow cone facing upwardly and engaged by a downwardly facing shallow cone carried by the spider.