Abstract: A mechanism for transferring movement between two reciprocating bodies, such as pistons or displacers (10, 11) comprises a crank or eccentric (12) and may be included in a Stirling or Vuilleumier engine. The crank or eccentric is connected to a connecting member (13) by means of a bearing or pivot (D). The connecting member (13) is connected to one (10) of the pistons or displacers via a second pivot (X) and to one arm (16) of a lever (15) by means of a third pivot (A). The pivots (A, D, X) of the connecting member (13) defines the vertices of a triangle. The other arm (17) of the lever (15) is pivotally connected to the other piston or displacer (11).The arms (16, 17) of the lever (15) may define an angle therebetween, and this angle may be selected so as to obtain a desired angle between the directions of the movements of the pistons, for example an angle of 90.degree..