Can a worm gear be used for linear motion as well as for rotation?
To be more specific. Suppose I want the worm gear to rotate as well as move forward, is it possible to achieve that ?
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Interestingly, this is the opposite of the desired behavior of zoom lenses. Optics design houses go to some lengths with cams and retainers to allow the lens to extend without rotation. You might try looking up old (1970s) zoom lens mechanical patents to see if there's anything there you could use.
But as to pure worm gears, since the worm only rotates if it's constrained from translating, you'd need some "secondary" worm that translated the "primary" worm at half the drive gear's linear rate. Even then I would be concerned that the tiniest error in step-down rate would cause catastrophic lockup.