You may spend a lot of time and money in a complex framework that makes the same full size futon to bed and vice verse and even includes a discus to arms, table or frame. But you can get the night of rest in a simple cot to the full size futon. You can use this cot itself a reason for sleeping, or expand on this basic frame with headboard and similar additions.
Buy wood in the local timber or facility improvement home. The flat is not expensive and easy to work with it, but it is possible to build this wooden cot using more expensive and attractive. All sanding wood surfaces. Need not remain perfect but should be smooth to avoid breaking chips or full size futon. If you want to paint the frame is easier to paint the wood prior to construction.
Put a plate on each small end of the frame full size futon. The outer ends should be aligned with the outer ends of the frame. The remaining plates arranged along the top of the frame, between the two plates already installed full size futon. Separate them equally, leaving small spaces between them to allow air circulation.