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In a description for ballscrews on a CNC, I saw two types of error listed:

  • Incremental error: < 0.0006"/ft
  • Cumulative error: < 0.0008" at 35"

What are these types of error measuring? What is the difference between them?

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The "incremental error" is the relative error in moving between two positions. (But only the USA would think of specifying a dimensionless quantity in "inches per foot" just to confuse people.)

If the screw is commanded to move a distance $x$ (in any length unit!) the distance actually moved will be between 0.99995$x$ and 1.00005$x$ (because 0.0006/12 = 0.00005)

But the cumulative error after several movements (or one long movement) is less than this: the above formula would give between 34.99825" to 35.00175" for a commanded total movement of 35", but the second specification says the actual distance moved will be between 34.99920" and 35.00080", which is about half the worst incremental error.

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  • $\begingroup$ Exactly. Which is why it's often best to drive to zero before moving to a new position. $\endgroup$ – Carl Witthoft May 16 '16 at 11:13

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