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Would it be possible --- yes. For $800 --- probably not.

You "might" be able to find someone to CNC something for you for less; however, you'd be hard pressed to do so. I recently had a 4500psi...

I'll go out on a limb and say yes this holds true for belts as well. The profile on a belt is designed to rotate a tooth around the axis of the pulley. The only places where the belt translates is...

Yes, it is possible. The tooth pattern would have to be a roulette (not exactly cycloidal due to the point of concern changing as the point of contact moves) though and not an arc (a sprocket tooth...

Not exactly. If you use a chain sprocket curve then the line of motion of the of the drive pinion will not stay parallel to the line of motion of the rack. Say that three times fast. Here's what I...

Joseph Ives used roller pinions in clocks. I'm not sure if the nexen rollers rotate on a shaft like Ives pinions did or not.