I can't tell you the mechanism by which cats purr. I don't think scientists have figured that out yet. However, I have figured out a mechanism by which I can purr.

Unfortunately, that involves a lot of airflow over my vocal cords on both inhale and exhale, so I can't keep it up for long. And the purr sounds slightly different on inhale versus exhale. And my purr is very fast and loud, compared to how slow and relatively quiet theirs can be.

I do suspect that my mechanism is similar to the one that cats use, because I've noted a similar difference in the sound of their purr on inhale versus exhale. But there are lots of other variables, too.

Unfortunately, our cats are kinda freaked out when I purr, so I don't do it often.