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There's basically three families of successful straight-pull rifles: Mannlicher started it all off, then Schmit-Rubin, and finally the Ross rifle, with the Lee-Navy as a short-lived dead-end.
Drawing of a Mannlicher M1886 Source
Swiss K31 Source
Three rifles in the Ross family. Source
Inner workings of the M1895 Lee Navy from its original manual Source
The straight-pull bolt-action rifle turned out to be just a step away from a self-loading rifle. If you're going to have the cost and complexity of a straight-pull, might as well go the extra mile and adopt a self-loading rifle. Many straight-pulls became self-loading or even automatic rifles.
The Mondragon rifle family (video) started as the M1894 straight-pull (video) but was not accepted. The design became a self-loading rifle adopted by the Mexican army. It was the first self-loading rifle adopted by a military.
1925 Italian Prototype by MBT (Metallurgica Brescia gia Tempini), only three were produced. They were incredibly over-engineered and the design was adopted to be semi and fully automatic.
Huot Automatic Rifle modified existing surplus Ross rifles with a gas piston to become a drum-fed automatic rifle. This was ordered by the Canadian military, but WWI ended before it was fulfilled.
Upvote:-1
Switzerland uses SchmidtβRubin. That's straight pull bolt-action rifle.