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DIY Roller Rack & Pinion - Need solution from experienced machinists

A cheap way to make roller pinion would be to use a worn out axial piston pump rotor ,cut a groove around the middle for the rack ..........use the pump pistons as rollers ..............these pumps are scrap when the valve face scores ,should be able to get one free.
Hello, sorry for the late reply:)
Actually i am looking for a side business, but i got the idea when i was thinking about to build a cnc steel tube cutter with rotary axis for 3m long tubes.
Ball screws are standard and there is nothing that will change that for precision machines that have high cutting forces, but first of all, the hobby ball screws that the most people buy have a accuracy error of 50 um/300 mm. This is not really that good. If you want better accuracy, you need ground ball screws, but they cost a lot more.
I have 3 meter long ball screws on my cnc router (2 long screws on the Y axis). Without the Rotating Nut system, the ball screws would bend a lot.
With the Rotating Nut system it works okay, but setting it up is not easy. The rotating nut housing/assembly has to be perfectly lined up. This might not be a problem for a industrial machine, where all parts are precisely machines, but for hobbyists who want to build a big machine its time consuming. Also, the most rotating nut systems uses belt drive.
Now, even i was thinking about to use the Roller pinion & rack system for a machine where are no cutting forces existent, i am more interested how it would work out in a CNC Milling machine, but to test it, i would need to build a machine :D. Who knows, maybe i will do it in some time, but first i would like to check if i can build such system with the machines i have here. Maybe i need to customize my lathe a bit, so that i can grind the rack, but i am currently thinking to machine the rack on a rotary axis on my cnc router. (short explanation: I put the rotary axis in vertical position to the spindle, like a vertical lathe. I use only the X Z and C (rotary) axis. So, the rotary axis will rotate and only the X axis will move linear. After one cutout, i will move the rack by the specific distance, lock it, and do the next cutout.)
The roller pinion rack system, might be interesting for people who want to build a machine with long travels, but also the costs "could" be a lot cheaper than a long ball screws, that will most likely have more accuracy error. But as i wrote earlier, for me most interesting would be to see how that system works on milling machines or generally machines with cutting forces.
PS @EmGo : I have talked with the guy who wrote that forum post. He helped me a bit, but then someone else found a couple days of time to create a app for Fusion 360 to create the correct rack for the pinion i want to use.
I will do some tests in next time. Today my harmonic drive will arrive, but i first need to setup my router for the 4th axis. (A axis or C axis)
Belt drive.
32 mm belt pushes 180 pounds over 30 feet, plus minus .004 when new, 15 years in holds .01. When it is middle of travel. Ends dead on.
Fast and cheap. Hobbyist is not going laser, even then the 21 foot machines run belts.
It’s a plasma, run chain/cable drive to avoid maintance. Our tube plasma is chain- it’s fine for that. Spend your money on powered front gate, gate adjustments, and outfeed. This is a sticking point on lasers on down the food chain.
Good luck with nexen it requires a few tenths of parallel and perpendicularism or it doesnt work
Sounds like the voice of experience...

My first reaction was that perpendicularity errors change the contact between pinion and rack from a line to a point, same as gears. However, given the "zero backlash" feature, they won't even mesh if there's bad perpendicularity?

Seems like parallelism errors just result in backlash, but at least they'd still work.

Practically speaking, not zero backlash.
However, given the "zero backlash" feature, they won't even mesh if there's bad perpendicularity?

Seems like parallelism errors just result in backlash, but at least they'd still work.
There's the main problem with cycloidal teeth. This is true of teeth teeth too, because they are generated from a rack, but let's just imagine the rack-and-pinion situation by itself.

A rack has straight sides. The curve of the tooth rubs against the rack teeth as it rolls. Since the rack has straight sides, it can be closer or farther from the pinion, or tooth-to-tooth errors in the pinion, you can just move the rack a little farther away but it's the same action. You'll get more backlash but the arc of the tooth will always roll smoothly against the straight sides of the rack, because they are straight. That's how you made the tooth shape, so it works correctly in reverse, too.

A cycloidal rack against pinion teeth is composed of two curves rolling against each other. So if one is moved out of position - parallelism or tooth spacing or twist or any reason - then it's a totally different situation. It's not just the same straight line moved a little farther away, it's a curve in the wrong place going the wrong way. And two pieces of steel don't like to be in the same place at the same time. So stuff interferes and bends.

If everything is perfect, the cycloid is better because it is all rolling, no sliding. Less friction. But this world is not perfect. Where the teeth are not in exactly the correct place as they mesh together, then an involute is much happier because it can just slide against that straight surface a little more. Or less, depending on the error. Involutes are way more forgiving.

(You can also make the case that an involute is just a special case of a cycloid, with one arc having an infinitely large radius, but now we're getting into lalaland, all that mathematics stuff. Makes me head ache so lets not go there.)