Problem is, if the machine is 'open', or even carries information into the past by appearing where it wasn't before, you're in exactly the same position as if the time-traveller could move out of it. If it's a closed box and the traveller can only travel forwards and backwards through it through the duration of its existence, then having a tough time seeing what use could be made of it, or even if you could tell it was actually a time machine. The idea that the curve has to be closed does present some possibilities (though presumably you could still leave one 'open' by deliberately not closing it).
Did you envisage it being a fairly large space in which people could travel back and forward at will but can only get in and out in their own time period (e.g. someone goes into the machine, travels into the future, then returns to the present and gets out - at a future time he'll appear in the chamber)?