Align a bone to a custom transform orientation and recalculate roll so that the bone Z axis points along the custom orientation X axis.
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Select object face.
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Create custom transform orientation (“Face” in this case) and keep it selected.
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Snap (Shift-S) → Cursor to Selected
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Enter armature Edit Mode.
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Either add a new bone or select an existing bone.
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Right click bone in edit mode and select “Align Bone to Transform Orientation”.
Or: F3 → “Align Bone to Transform Orientation”
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Now the bone sits orthogonal on the selected face and is rolled in a way that its Z axis points along the X axis of the custom transform orientation.
