This bridge is a replica of the bridge which crossed the Galgewater here till 1817. The current bridge is build in 1983 and is a wooden, double drawbridge. On the northside of the bridge the mill De Put is a replica of the mill which stood here from 1619 till 1640. On the other side there has been a similar mill, owned by the family of Rembrandt van Rijn, after who the bridge is named. Rembrandt van Rijn was born and raised very close by in the Weddesteeg.
Info: http://nl.wikipedia.org/wiki/Rembrandtbrug (Dutch)