Both AutoCAD and Revit contain the function "nudge" - for nudging, pushing of selected objects in a certain distance using the respective arrow-key on your keyboard.
It is an inaccurate operation not suitable for moving the drawing geometry, but it can be useful e.g. for fine-tuning placement of texts, annotations, legends, etc.
In AutoCAD you can invoke nudging of grip-selected objects by pressing the combination Ctrl+arrow (up, down, left, right), in Revit just press the arrow key.
The nudge step size depends on the current zoom level - so it is measured in "pixels" rather than in drawing units. In AutoCAD Snap mode (F9), the nudge step size is equal to the current snap size (see SNAPMODE and SNAPUNIT). Using your cursor keys, you can nudge objects in a fixed relative distance, e.g. 1 mm (unlike absolute Snap).
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Please use these tips at your own risk. Arkance Systems is not responsible for possible problems that may occur as a result of using any of these tips.