I have never heard of anyone making their sale contingent on their purchase. The other way around is common, although often unappealing to sellers for obvious reaons. As a buyer, I would find that option pretty unappealing. It seems like you could easily get stuck in a nasty loop of contingencies between all of the parties involved.
I've known several people to sell one house before buying another. You can get look into a short-term rental. You might consider whether a friend or relative would give you a place to stay for a bit. You would probably also have to put much of your stuff in storage for a bit.
If you can afford to buy without selling first, you can also simply buy something else and move before marketing your current house. I am doing this in the next couple of months because inventory is so limited in my market I refuse to be forced into buying something I really don't like due to time constraints.