I was asked about binding tight curves by Shisomama, who is attempting to bind baby bibs with a plate binder. Unfortunately, it is extremely difficult (if not impossible!) to bind tight curves with this type of binding attachment. As you can see here, the binding enters the attachment at about a 45 degree angle and is then straightened out well before it gets under the needle. This type of binder is best for straight or slightly curved work.
Then we have the right-angle binder which works very well on tight curves and rounded corners. The fabric enters the binder at a 90 degree angle and does not straighten out until just before it goes under the needle. This type of binder is attached to a commercial needle plate (which fits most single-needle machines). It also requires a special feeder and foot. This particular set came with a standard binding foot (on the left) and a compensating foot (right).