Hard to think of practical application for a thread of that form.
As for the video, once I'd endured the irrelevant ads including an American one for a product allegedly sold in the UK, I gave up on the video itself even before the machinist with St. Vitus' Dance had even reached the far side of the woods. I had gathered he was supposed to make something like the screw in the catalogue picture he showed us below The Sign of the Swinging Lamp.
I can't be doing with gimmicks, over-acting and time-wasting.
Zig-zag multiple threads though? I suspect the booklet image was an example to show what the company could make, not what it normally made. Hard to think of any real use of such a thread, not already met in simpler ways. Nevertheless, over the years designers did create some wonderful drives for specific results, including square and elliptical gears, which give continuous rotations with continually-alternating ratios.
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A variation of that "zig-zag thread", with smooth transitions between directions, might give a continuously reversing drive of several rotations per stroke; but would still need some form of homing mechanism. Otherwise it shows an exercise in Advanced Turning and Metal-Puzzle Making, but then what?
Overlapped threads of both hands though, are real……
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These are on reversing lead-screws, having left and right-hand, single-start threads of the same pitch on the same shaft.
The two threads meet in a short but smooth return at each end of the shaft. The "nut" on the examples I saw is really a follower, typically a pivoting, lozenge-shaped block or a roller; but other machines might use perhaps a recirculating-ball nut.
I have seen such lead-screws on special winches, driving a fairlead back and forth to wrap the "cable" properly over several layers. The pitch is that of the "cable" wrapped fully, in lateral but uncompressed contact; and the lead-screw is obviously geared to the drum in the correct ratio. (The covers probably hid timing-belts and toothed pulleys.)
Such a screw allows relatively very long strokes at constant speed in a very compact format. So another possible application might be driving a shaper or planer, provided having no "quick return" is unimportant, although the stroke cannot be varied except by changing the screw. It would though spread the wear evenly along the whole length of the ram and ways. It might be one way to convert a manual to powered shaper, and making the screw (best milled) would be an interesting exercise.
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(Some winches using conventional wire-ropes guide the base wrap by a single-start "thread" of semicircular profile with attenuated crests, of pitch equal to cable diameter, cut in the drum surface. Once that first wrap is complete, its own surface guides the return wrap.
On the particular winch I have operated, with a threaded drum, the fairlead is simply a hard, flat plastic strip the length of the drum. This works because the distance to the block is an open span of some 10 – 15 metres. The reversal used to create quite a shock as the cable jumped up onto the foundation layer, greatly reduced by fitting a snubber – just a convex plastic block – at each end to ease the cable over. )