This paper presents a first order analysis of four types of overdriven free-displacer Stirling machines. All the presented types of machines can work as refrigerating machines, prime movers or heat exchange accelerators depending on parameters such as the hot to cold source temperatures ratio, the nondimensional mass of working gas in the machine, the displacer rod to displacer cross sectional area ratio, the corrected dead space to piston cylinder volume ratio and the displacer to piston cylinder volume ratio. In its analytical form this theory holds for machines at low speed as it is assumed that the piston displacement can be neglected during the displacer movement duration. This analysis may be used to find the conditions and values giving either the best theoretical refrigerating cycle or the best theoretical prime mover cycle, the associated reference work, reference time, efficiency and heat quantities involved. A table gives the analytical expressions and the limiting values of the main parameters for the four different types of Ringbom machines considered. The preliminary design of a Ringbom prime mover is then presented. The main parameters influences are predicted and the magnitude of work, rotational speed limit and efficiency are obtained.