In a reciprocating-piston machine, in particular a refrigerant compressor for a motor vehicle air-conditioning system, including a machine shaft, a plurality of pistons are arranged, at the same distance from the machine shaft, on a cylinder envelope defined by the axes of the pistons and extending around the machine shaft, and an annular pivoting disc which is driven by the machine shaft and which engages the pistons via a joint arrangement, the joint arrangement has an at least partially spherical receptacle, in which at least one sliding element structure is arranged moveably relative to the associated piston and relative to the pivoting disc, including a first sliding element having a first sliding face in the form of a spherical segment with a first geometric center (M.sub.1, M.sub.3), and a second sliding element having a second sliding face in the form of a spherical segment with a second geometric center (M.sub.2, M.sub.4) arranged at a distance from the first geometric center.