The linkage was typically used with early beam engines before the development of crossheads that would allow the piston connecting rod to always move linearly while directly driving the crankshaft.
The photo shows the vertically oriented cylinder driving the end of the beam (which moves in an arc) via a Peaucellier linkage. The other end of the beam then drives a rotary power takeoff shaft via a conventional crank.
These engines were operated at low speeds and the linkage helped extend their useful life to many decades at the expense of complexity and increased frictional losses.
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