Multiple free-piston Stirling (FPS) machines are arranged in a group and connected for preventing or minimizing vibration. A first set of identical beta FPS machines are arranged in a mechanically co-directional orientation and configured to reciprocate in thermodynamically synchronous reciprocation with each other. The first set has axes of reciprocation intersecting a first point. A second set of beta FPS machines are arranged in a mechanically co-directional orientation that is the same as the mechanical orientation of the first set of beta FPS machines and are configured to reciprocate in thermodynamically synchronous reciprocation with each other but in thermodynamically opposed reciprocation to the first set. The FPS machines of the second set are identical to the FPS machines of the first set and have axes of reciprocation intersecting a point, which may be a point at infinity.