What was lincolns motivation behind the emancipation proclamation and the timing of its delivery?
Lincoln had several reasons for signing the Emancipation Proclaimation. By redefining the war as one that was now to free the slaves. First, it decouraged slaves to run away from their masters, thereby depriving the south of the manpower slavery provided. Second, he knew that by phrasing the proclaimation like he did, it wouldn't drive away the border states, because only those state in rebellion were technically affected by it.
The main reason was that by saying the north was on a mission to free the slaves, he was able to keep Europe out of the war. With the war now being fought to end slavery, France and Britain, two countries who had already emancipated their slaves, could never support the Confederancy.
Lincoln timed his annoucment to coencide with a strategic victory by the Union so it didn't seem like a last cry of desperation by a losing cause. He wanted it to to be made from a position of strength.