If your Z axis is moving in the opposite direction, go into Mach3, click on config, ports & pins, then click on the motor outputs tab. You will see the axes labeled on the left and the parameters labeled on the top of this dialog box. Toggle the dir low active for the z-axis.
What if I'm having the same issue on a different axis?
You can follow the same procedure as with the z-axis. When you get to the motors outputs tab, toggle the dir low active checkbox for the axis that you would like to change.
If you are using another control program, let me know and I will add the recommended action here.
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The z-axis on my assembled machine is reversed