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I principle because many movements can be derived from the 3 or 4 fold machines.

4- Fold would mean the normal 3 Cartesian axises and a rotation. What do you need more than that.

Earlier there was a 2 1/2 fold machine, but that was because of the difficulty of making the third axis smooth. The X and Y axis were smooth, but introducing the Z axis was difficult, so for a time the Z axis could only be done in steps like south east Asian farming shelves.

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