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Don't be afraid to step in and take charge when needed. I've seen many successful teams with strong driving mentors, and I've seen many lackluster teams with mentors who sit in the background. Of course there's probably also a number of counter-examples. Personally, as a mentor I like to see results. I am not the mentor who asks questions all day long without ever providing answers. That does not lead to results.

I believe that when it comes to quality, good work comes from good examples. If you let students entirely run the show, yes they may come up with something decent on their own but it would probably rarely be of the quality it would be if an experienced mentor showed them better methods or designs. Very few people every got smart and experienced all on their own. It helps to show them certain ways to do things, and why their ideas may not work, or may be better implemented by some other means. To me, it's not smart to just let the students do whatever they want and only be a mentor when they call on you. You'll see more success my taking more of a leadership role.

The show part is critical when it comes to manufacturing methods and tool usage/safety especially. I would have never learned to run machine tools from someone just asking me questions or doing it for me.

The do part is fine, but make sure what you're doing is supplemental rather than replacing student work. There are certain things I believe students don't absolutely need to be involved in every aspect of. Also, sometimes there are not enough hands to go around, and the mentor doing things can be a big help.

For a specific example of mentors stepping in or not, let me talk about the 696 minibot from this prior season. We let it be an entirely student-run subsystem of the robot. And to be brutally honest, it failed rather miserably. The students did not understand the Physics involved, and were all new students to the team without prior experience. There was very little mentor guidance. To prove a point to myself and others that a fast efficient minibot could be designed and constructed easily with minimal difficulty, I went and built one on my own one night, and brought it in to show the team. They had no perception that it could be so easily done until seeing it. They were not familiar with things like strong magnets, and removing gear heads from motors. It was too late for them to change course on their plans, but we ended up using my minibot on several partner teams' robots with great success, and ended up winning the Coopertition award. This was a great experience for the students in working to install a minibot on other teams' robots when their own had failed. They got to work with teams from other countries even who hardly spoke any English. Did the students learn how to build a great minibot on their own? No. But did they learn that it could be done and get a new spark of inspiration to wipe out the discouraging failure of their own? Yes. Did they learn more than if I had done nothing at all? Absolutely.

Whatever you do, just ask yourself "would the team still function without me, or would it collapse?" If it would collapse without you, you're doing to much yourself without showing others. If it would still function without you, you're doing it right. It needs to be a self-running machine.