While using Vex for a prototyping project, I realized that Vex had no way to reproduce the characteristics of a lead screw, and started thinking about what a Vex one would look like. I think it would be a pretty cool addition to the Vex product line! I was thinking something along the lines of…
-Made in ~2" segments, with square hole through the center to string multiple pieces together
-Would serve as the long demanded “shaft-coupler-piece” better than anything currently available
-4 threads, impossible to connect improperly using the square hole
-Maybe could double as a multi-thread worm gear, for increased ratio flexability (don’t know enough about tooth geometry to know if this one is viable.)
This is an excellent idea for the Vex product line, and I would certainly buy a few
But there are a few details that matter…
If you think about how something like this would be used, it is clear it will operate under high load much of the time; Think arm lifters and the like. I would expect mostly compression loads, since tension loads could be easily handled using high-strength chain or a cable & wench.
If you place a strong compression load on a Vex axle, it will almost certainly deflect a bit. If the lead screw is slid over an axle in 2" segments, the deflection will happen between the segments causing small gaps to open. These gaps will jam the nut and the whole system would be unreliable.
If the lead screw is plastic, it will be at risk of damage due to contact with steel (in your parts box or in a competition). A damaged segment would be a further jam risk. This risk applies to the existing Vex rack, but since racks don’t completely “capture” the pinion the way a nut captures a lead screw, racks and pinions tend to be a bit more forgiving.
If you go with a 4-start lead screw as you suggest, it will simplify assembly, but it will have a pretty aggressive pitch. This will reduce the force multiplier and introduce a much greater risk of back-driving. That probably means you would not direct-drive the lead screw from a motor, instead using some gear reduction between the motor and the screw.
As for the nut, if it is made as your examples show, you’ll get a large contact surface between the nut and screw. This will handle high loads, but will also present significant friction, reducing the overall efficiency. The nut’s threads could be a few rows of nylon nibs rather than a solid thread.
Perhaps the nut could be two identical halves to be bolted together onto Vex plate. That would allow the builder to add a shim between the two halves to reduce the friction if they could afford a bit of play. A split nut also makes it easy to correct “phase” errors so you wouldn’t need a 4-start pitch.
So, for me, it seems like the best bet would be to sell steel acme thread rod in 12" or 18" lengths (1/4-16?), along with a coupler to adapt it to the Vex 1/8" square axle. The nuts would look like your 2nd example, probably made of brass or nylon, but would be split into 2 pieces to simplify disassembly/reassembly and allow some option for friction -vs- play.