Miniature punch press - video

[Toolmaker51]

A "real" press might run straight toothed dogs, angled sprags, plate & disc...depending on tonnage and press type. Maybe needle clutch if there is a way to actuate at TDC of the crankshaft.
Since [the model] it's hitting light foil, at relatively low speed, a number of possibilities exist. Biggest restraint; scale of parts to attain running fit with actuation.
https://en.wikipedia.org/wiki/Clutch
I hate to call it a model, it is a true punch press, just tiny. Such things always remind me of aeronautic engineer in "Flight of the Phoenix", defending free flight [small scale] planes versus models and toys.

After a plane crash in the Sahara, one of the survivors says he's an airplane designer and they can make a flyable plane from the wreckage.
The Flight of the Phoenix (1965) - IMDb