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I am currently making a stepper motor controller based on this schematic

schematic however I was wondering about the difference between half and full stepping and what would be the best method for a stepper motor in a CNC machine.

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For a bipolar motor such as you are using, the two coils can each be driven positive or negative. This gives 4 combinations, and these combinations are sequenced to give (relative to a cycle) 90 degree phase shifts. But it's possible to do an intermediate drive, where you set one current or the other to zero as a part of the sequence. This is called half-stepping, and you can google for the details.

The advantage to half-stepping is that it will give you twice the shaft angular resolution per half step compared to what you get in full step mode. The disadvantage is that you get half the torque. A second advantage to half-stepping is that it often has less problems with resonance at high step frequencies.

Which would be better? Depends entirely on the motors, the physical setup and the profiles you want the tool to follow. If the resolution available with full step is adequate, stick with it. If you must have the resolution, go with half steps and use a slower tool motion/acceleration. If you need both, get a bigger motor.

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