Thank you very much guys for your help and valuable information. This is a very friendly community.

However, I still have a problem of... a weird nature. Looks like now I can apply a fillet on that object with a sharp corner from the scene I attached to my post (even though I couldn't do it before!), but the fillet does not compute for the object fixed by BurrMan. I'm very confused about what is going on. I think I must be doing something terribly wrong.

What I do is I open the hinge_cusp.3dm file, select the object, select the fillet command, enter the radius (0.3) and nothing happens. There's no "Calculating..." message or anything. The fillet is not created after I press "Done".