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I am trying to animate a knob. The knob is on a flat plane, but that plane is angled. How can I rotate the base of the knob (red line) so it remains parallel to its base? I've tried aligning the view to the top and changing the cursor orientation, but it doesn't work the way I want it when I just want to rotate on the z-axis for example.

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If your knob is already aligned with your plane (as you said): Set the Transformation orientation to Normal, then select your "base face" (Edit Mode, Face Selection) and create a new Transform orientation. This gives you a new transform orientation. Then switch to Object Mode and rotate your knob along the z axis (which now corresponds to the face normal of your previously selected face). This should give you a perfect rotation in which the knob always sticks/keeps aligned to the surface.

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