Mechanical power transmission over a variable distance

Does anyone have a good method for transmitting mechanical power over a distance like a chain or belt, but where the distance between pulleys or sprockets is highly variable as the mechanism moves?

There are a few good options for this, but most require significantly more moving parts. I recently designed something similar that was a conveyor to this:


This requires 2 more idler rollers, but they are fixed mounted, one to the static piece, and the other to the moving piece.

Another option is simply a large variable take-up, also very common in conveyors.

Each have their benefits and drawbacks, and either can be used with belts or chain.

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One nice and easy way is to just use a hex shaft or something along the axis of movement, then hex broach some Oilite to act as a power-transmitting linear bushing. If you need a more off the shelf solution, square shaft and bushings may be easier to find - plus you can get square carbon fiber shaft, which’ll be pretty light and compatible with plastic (maybe even 3D printed) bushings, assuming you don’t need to transfer too much torque. I think people made some 3D printers that used the square shaft + bushing concept, but I can’t find any pictures.

Here’s a really dumb idea:

Two tangent runs of double-sided timing belt, where the outside teeth from the two belts interlock eachother:

Here is an even dumber idea:

Two chain runs with a sprocket between them, but only fixed to one rail. Sprocket acts to transmit torque between the two chain runs. Fancy things to improve wrap at your own discretion.

You could also do the drive-shaft thing - two telescoping features (like 1/2in hex and 3/4in hex tube) with a bevel gearset on each end.

In industry you’d likely use a spline shaft and bushing, which you could mimic using a bit of hex shaft and a (plastic for slipperiness) hex hub. Unfortunately you’d need to attach each end to a miter gear to make it drive two overlapping conveyors.

In an FRC context, I’d just use two motors.

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