I've actually seen a trisection device with no moving parts at all. It's basically a strip with one end having square and circular attachments at the end. By placing the object in the right position relative to a given angle, the trisectors of the angle are identified.
The Archimedean trisection (using the marked straightedge) algebraiclly solves any cubic equation with three real roots, for the solution of such an equation always reduces to an angle trisection via Viete's formulation. So the method can be adapted to another old "impossible" (with unmarked straightedge and compass) problem, the construction of the regular heptagon.