The mechanical configurations of Stirling engines are generally divided into three groups known as the Alpha, Beta, and Gamma arrangements. Alpha engines have two pistons in separate cylinders which are connected in series by a heater, regenerator and cooler. Both Beta and Gamma engines use displacer-piston arrangements, the Beta engine having both the displacer and the piston in an in-line cylinder system, whilst the Gamma engine uses separate cylinders.

The Alpha engine is conceptually the simplest Stirling engine configuration, however suffers from the disadvantage that both pistons need to have seals to contain the working gas. An excellent step-by-step animated display the operating principles of this basic alpha is shown on the Whisper Tech (New Zealand) website. Other excellent animations have been done by Matt Keveney, including the V-type Alpha stirling engine.
Andy Ross of Columbus, Ohio has been developing small air engines with extremely innovative Alpha designs, including the classical Ross-Yoke drive and more recently a balanced "Rocker-V" mechanism, as shown below.


Matt Keveney has done an animation showing clearly the principles of operation of an Alpha stirling engine using the Ross yoke linkage. Andy Ross is in the process of publishing an article on the model Climax locomotive that he recently built using a small Rocker-V engine. I am delighted to have available a preprint of this article "A Class A Climax Locomotive". Some photographs from this article emphasizing Andy's excellent craftsmanship can be seen in the following: (Climax Locomotive, Open Cabin, Rocker-V engine bottom, Rocker-V engine top).
The Alpha engine can also be compounded into a compact multiple cylinder configuration, enabling an extremely high specific power output. A schematic diagram of this configuration is shown below. Notice that the four cylinders are interconnected, so that the expansion space of one cylinder is connected to the compression space of the adjacent cylinder via a series connected heater, regenerator and cooler. The pistons are typically driven by a swashplate, resulting in a pure sinusoidal reciprocating motion having a 90 degree phase difference between the adjacent pistons.

Whisper Tech in New Zealand have developed a modern four-piston wobble-yoke machine for multi-purpose power generation applications, as shown below. Refer to their website for further details of this engine. They also have an excellent animated display of the unique wobble-yoke drive that they have developed for this engine.

Another design of this type is the STM 4-120 engine was made by Stirling Thermal Motors. A cutaway diagram of this engine is shown below. Unfortunately this company has recently ceased development of this engine which had the unique capability of controlling output power by means of varying the swashplate angle.

Recently William Beale of Sunpower, Inc has come up with an ingenious configuration combining a four cylinder free-piston alpha engine with a gas turbine output stage, as shown in the following schematic diagram:

The four cylinders are physically arranged with a 90 degree phase difference with each piston connected to a gas compressor. The gas compressors are then used to drive a gas turbine expander as shown. A prototype machine of this configuration is currently being evaluated. The main advantage of this system is the promise of a high specific power and most important, high reliability and life resulting from the absence of heavily loaded moving parts, since there are no side loads on any sliding bearings.
The sketch shows single acting gas compressors for simplicity, but the actual machine uses double acting compressors so that there are eight gas pulses on the turbine for each cycle of the four cylinder machine.