The crank drive is perhaps the simplest of all mechanical drives used in kinematic Stirling engines. It is relatively easy to build and is conceptually easy to design.
However, its main disadvantage is that it creates lateral forces on the linkages. This is in contrast to the Ross Yoke, which creates very little lateral force.
The figures below illustrate the crank drive:

Design Procedure
If you want to size a crank drive for your Stirling engine, the procedure is simple:
1. Choose your desired piston stroke length. Call this SL.
2. The radius R = SL/2
As shown in the figure above the angular position of the hot side piston is 90 degrees ahead of the cold side piston. 90 degrees is the phase difference for maximum engine power, assuming an alpha engine. Note, for a beta and gamma engine, the optimal phase difference is not 90 degrees. Fortunately, the crank drive mechanism allows for flexibility in choosing different phase angles. However, the crank drive is perhaps better suited to a gamma engine than a beta engine.
With a crank drive, the motion of the pistons will be close to sinusoidal. They will be almost perfectly sinusoidal if R is much shorter than the linkage arm which connects to the pistons. Also, an R length much smaller than the linkage arm length results in lower lateral forces.
Here’s a video of the crank drive I used in my Stirling engine project:
This website by Zig Herzog analyzes some of the different drives for Stirling engines:
http://mac6.ma.psu.edu/stirling/drives/index.html
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