When I create new axes for a group, the blue axis is invariably pointing downwards which means that when I bring components into the group they will be upside down. I have been using SketchUp Make for a long time, but I’ve never quite got the hang of axis tool. I’m using SketchUp Make (2015) on a Mac.
When you change the axes in the component, you control where you want the red and green axes. Depending on how you move them, it’ll affect the direction of the blue axis. If you try again, after the first click (to pick the red axis), you can move your mouse around to choose the green axis and you’ll see where the blue axis will end up as well.
Here is a gif of what @quantj is describing.
After you select the origin point (first click) and then the red axes (2nd click) the third click will set the green axes and the blue axes. I am clicking when you see my cursor pause. It is best to just keep a careful eye on the visual feedback before clicking the third time when setting the axes.
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Thanks so much for your response to my inquiry. I finally see how something works that I should have known years ago!