An invention that could replace hose clamps and maybe screws and nails: roulette-bristle slotted tape.
If you wrap sticky tape around a thing, you can form a sort of hose clamp holding the thing, but the tension in the clamp is limited by the fact that the stickiness of the tape prevents the tape from sliding not only to loosen, but also to tighten. (The constant-tack nature of most sticky-tape adhesives also means that tape joints like this will tend to creep over time if under stress, losing whatever tightness they may have originally.)
Velcro has similar behavior, but it doesn’t creep. It does loosen a bit by a fixed backlash distance upon being first attached, though.
In both cases, the clamping force is limited to the force you applied pulling the tape tight when you first made the joint, multiplied by the number of rounds the tape goes around.
But suppose instead that the bottom layer of tape has an array of round rods sticking out of it, like widely-spaced Bristle Blocks, which fit through round holes in the top layer of tape. This eliminates the creep and backlash problems, and also potentially gives you a bit of mechanical advantage: if the rods don’t quite line up with the holes so you have to bend them backward to fit through the holes, then the rods form a sort of ramp that tightens the tape as it slides down them. (If it so happens that they don’t quite line up in the other direction, the ramp loosens the tape, instead.)
This is a bit awkward, though, because the holes travel in an involute of the shape you’re wrapping the tape around, while the rods, so far, are straight. But, with things like a 3-D printer, you could form the rods in an involute shape so that the holes in the tape naturally slides over them with no resistance.
If you skew them ever so slightly from perfect involutes, they naturally become the ramps I earlier suggested you could bend them into; this can serve to tighten the tape as it closes over them. It also means that tension on the tape tends to lift it up along the bristles. If the final upper-tape-thickness or two of the bristle is a backward ramp instead of a forward ramp, then the tape will instead tend to stay there under tension.
If the holes are more like lengthwise slots in the tape
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then there is some slop in where the bristles can pass through. If you make the spacing of the bristles along the bottom tape slightly larger than the spacing of the holes along the top tape, then the tape will stretch progressively as you wrap it over further and further bristles; the slot shape then can allow the earlier bristles to slide back in the slot as the tape stretches, avoiding the problem with sticky tape.
Ultimately you could have the tension of the tape held by the final, say, fifteen rows of bristles; if you are able to wrap the tape separately over each row (perhaps with a curved tape shape and bristles more resembling a cycloid than the involute of a circle) then you could apply the downward force on the tape against only one row of bristles at a time. (Ideally the rows would be diagonal so that this is a smooth experience.) If the ramp of the bristles, relative to the involute or cycloid or whatever, is 20:1, then the row of bristles gives you a mechanical advantage of 20:1, while the 15 rows of bristles give you an additional mechanical advantage of 15:1, for a total of 300:1.
This is better than the mechanical advantage of a screwdriver with a 25mm-diameter handle driving a 1-mm-thread-pitch screw, which is only about 79. It’s more like using a small 5-cm-long wrench to drive a 1-mm-thread-pitch screw. That is to say, this is a fastening device that could easily replace the screw in many applications, unless I’m overlooking something.
If you can wrap the tape, say, five times around, before putting the holey part on top of the bristley part, then you have potentially an additional 5:1 mechanical advantage, which is like using a 25-cm-long wrench to drive a 1mm-thread-pitch screw. I’m not quite sure how you could do this, but I suspect it’s possible.
If you have lateral freedom in where to connect the holey tape and the bristley tape, the aforementioned diagonality of the bristle rows can give you fine-tuning of the distance, with greater precision but less convenience than a screw. If the bristles are 1mm diameter with 2mm spacing and the rows are 20 bristles wide, then each bristle to the left or right in a row could be 50μm ahead or behind of its neighbor, providing you with that degree of fine-tuning of the distance, at the cost of some loss of strength (or doubling the width of one of the tape components).