csrc, Worm / wormwheel gear reductions are good for high gear reductions. They do not like speed. This arrangement is not really "gearing". It is actually functioning as a screw. Gears roll usually on an involute surface Whereas screws and worms slide against nuts or wormwheels.
If what you need is slow, accurate and fairly backlash free motion, worm gear reductions are fine. Some examples are the workpiece rotation in fairly slow rotary motion like gear hobbing / shaping or rotary tables etc.
The only linear motion using worm reductions I remember was the slow movement of very large boring mills etc.
Hope that helps
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